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1 hour=60minuteshence274/60=4.577 hours

1 hour=60 minuteshence720/60=12 hours

Sec 20= 1/cos 20=1/sin 70cot 70= cos 70/sin 70cosec 20= 1/sin 20= 1/cos 70

(1+sec 20 + cot 70)=1+1/sin 70+ cos 70/sin 70take LCM(sin 70+1 + cos 70)/sin 70similarly(1-cosec 20+ tan 70)= (cos 70-1+ sin 70)/sin 70

multiple both equations

(sin70 cos70- sin 70+sin^2 70+ cos 70-1+sin70+cos^2 70- cos 70+ sin70 cos 70)/ sin70 cos70

(2sin 70 cos 70)/ sin70 cos 70=2

According to the trigonometric identity,tan70=tan(20+50)tan70=(tan20+tan50)/1-tan20tan50tan70-tan20tan50tan70=tan20+tan50Also tan70tan20=tan70cot70=1Hencetan70-tan50=tan20+tan50So tan70=tan20+2tan50

tan 70 = 2.74 tan 20 = 0.36so, 2.74 * 0.36 = 0.9972

As we all know,According to the trigonometric identity,tan70=tan(20+50)tan70=(tan20+tan50)/1-tan20tan50tan70-tan20tan50tan70=tan20+tan50Also tan70tan20=tan70cot70=1Hencetan70-tan50=tan20+tan50So tan70=tan20+2tan50

140 = 7 × 2² × 5

156 = 2²x 3x 13

3825 = 3² x 5² x 17

Tan70 = tan(60+10) use the identity : tan(a+b) = (tan(a) + tan(b))/(1-tan(a)tan(b)) so, tan70 = (tan60+tan10)/(1-tan60tan10) tan70 = (sqrt(3)+tan(10))/(1-sqrt(3)tan10) ... (1) tan50 = tan(60-10) use the identity : tan(a-b) = (tan(a) - tan(b))/(1+tan(a)tan(b)) so, tan50 = (tan60-tan10)/(1+tan60tan10) tan50 = (sqrt(3)-tan(10))/(1+sqrt(3)tan10) ... (2) therefore, the value of tan70 - tan50 = (sqrt(3)+tan(10))/(1-sqrt(3)tan10) - (sqrt(3)+tan(10))/(1-sqrt(3)tan10) if that simplied becomes, we get tan70 - tan50 = 8tan10/(1-3tan^2 10)

now, look at the original question above is , sin10-sin50+tan70 which similar with tan70 - tan50 + tan10. (the value of tan70-tan50 already done) so, tan70 - tan50 + tan10 = 8tan10/(1-3tan^2 10) + tan10 = (8tan10+tan10-3tan^3 10)/(1-3tan^2 10) = (9tan10-3tan^3 10)/(1-3tan^2 10) = 3 (3tan10 - tan^3 10)/(1-3tan^2 10)

then, remember that there is a formula in trigono : tan(3x) = (3tan(x) - tan^3 (x))/(1 - 3tan^2 (x))

therefore, the calculation above can be simplied becomes 3 (3tan10 - tan^3 10)/(1-3tan^2 10) = 3 tan(3*10) = 3 tan30 = 3 * 1/3 sqrt(3) = sqrt(3)

P(x)= 5t^2+12t+7

=> 5t^2 +5t+7t+7

=>5t(t+1)+7(t+1)

=>(5t+7),(t+1)

=>t= (-7/5) or t= (-1)

Sum of the zeroes

= alpha + beta = -b/a= -12/5

Product of the zeroes l=alpha *beta = c/a= 7/5

f(x)=5t^2+12t+7; =5t^2+5t+7t+7; 5t(t+1)+7(t+1); (5t+7)(t+1); 5t=-7; t-7/5; t=-1

-12/5 , 7/5 is the correct answer of the given question

sin30=1/2sin45=1/√2cos60=1/2cos30=√3/2cosec90=1cot90=0sin60=√3/2tan30=1/√3Hence put in the equation1-1/4/1+1/2*(1/4+3/4/1-0)÷(√3/2*1/√3)=3/4/3/2*(1/1)÷(1/2)=2÷1/2=2*2=4

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Sin60*cos(90-60)+sin30.cos(90-30)

Sin60*sin60+sin30*sin30

Sin²60+sin²30

{√3/2}²+1/4

3/4+1/4

(3+1)/4

4/4

=1

n,n+ 1 andn+ 2 are three consecutive positive integers.

When n = 2,

n(n+ 1) (n+ 2) = 2 (2 + 1)(2 + 2) = 2 × 3 × 4 = 24.

Thus,n(n+ 1) (n+ 2) is divisible by 24.

P = { 2,4,6,8}

Roaster formP={ 2,4,6,8}

(2) is the right answer

2-is right answer of ouestion

2 is the right answer

required answer is equal to 4

(a) 2 is the right answer.

option (2) is correct

Tan70 + Tan20= K cosec40Tan90= K cosec40

tq

Sin 50= cos 40as sin(90-50) = cos 40change cosec and sec into sin and costhen after putting the valuessin 50/sin50+cos50/sin50-(4*cos50*1/sin50)1+1-42-4= -2Answer

2(cos[90-23]/sin23 - tan[90-50]/cot50 = 2(sin23/sin23) - cot50/cot50=2x1-1=2-1=1

Sin84° sin48° sin24° sin12°= 1/4*(2sin84° sin24°) (2sin48° sin12°)= 1/4*(cos60°- cos108°)(cos36°- cos60°)= 1/4*(1/2 + sin18°) (cos36° - 1/2)= 1/4*(1/2 + (√5 - 1)/4) ((√5 + 1)/4 - 1/2)= 1/4* ((√5 + 1)/4) ((√5 - 1)/4)= 1/64 * (5-1)= 1/16 Formula used: cosA - cosB = 2sin((a+b)/2) sin((a-b)/2)Values of sin18° = (√5 - 1)/4 and cos36° = (√5 + 1)/4

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Explanation : P = { x | x is an even natural number. 1<x<10} = { 2 , 4 , 6 , 8 }

Solution : { 2 , 4 , 6 , 8 }

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A decimal number is the number after point

A decimal number is a number with a decimal point in it, like these: 1.5 .6 3.14. The number to the left of the decimal is an ordinary whole number. The first number to the right of the decimal is the number of tenths (1/10's). The second is the number of hundredths (1/100's) and so on.

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a decimal numbers is a number which have point in it

decimal number basically means a numberafter appoint may be at any place

1/4 as decimalis 0.25

bhai nahi pata khud hi kar le

b option is right

because sin 60 = √3/2sin 30 =1/2cos 30= √3/2

cos 60= 1/2put these values in this

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Length of the side of equilateral triangle = aPerimeter of the signal board = 3a = 180 cm∴ 3a = 180 cm ⇒ a = 60 cmSemi perimeter of the signal board (s) = 3a/2Using heron's formula,Area of the signal board = √s (s-a) (s-b) (s-c) = √(3a/2) (3a/2- a) (3a/2- a) (3a/2- a) = √3a/2 ×a/2× a/2×a/2 = √3a4/16 = √3a2/4 = √3/4 × 60 × 60 = 900√3cm2