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((a+b)(a+b)+(a-b)(a-b))/(a*a+b*b) = (a*a+2ab+b*b+a*a-2ab+b*b)/(a*a+b*b) = (2a*a+2b*b)/(a*a+b*b) = 2(a*a+b*b)/(a*a+b*b) = 2

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cotA - 1 / 2 - sec^2A = cotA / 1 + tanA

LHS= cotA - 1 / 2 - sec^2A= (cosA/sinA - 1) / 1 + 1 - sec^2A= [(cosA - sinA) / sinA] /1 - tan^2A= [(cosA - sinA) / sinA] / [1 - sin^2A / cos^2A]= [(cosA - sinA) / sinA] / [(cos^2A - sin^2A) / cos^2A]= (cosA - sinA) / sinA X cos^2A / (cosA + sinA) (cosA - sinA)= cos^2A / sinA (cosA + sinA)

RHS= cotA / 1 - tanA= (cosA / sinA) / (1 - sinA/cosA)= (cosA / sinA) / [(cosA - sinA) / cosA]= cosA / sinA X cosA / (cosA - sinA)= cos^2A / sinA (cosA + sinA)

LHS = RHSHence proved.

B=90-Acot(90-x) =tanxtherefore, cot(90-A) =tanAtherefore, TanA=3/4

cotB=3/4=>tan(90-B)=3/4=>tanA=3/4. {A+B=90}

(cosecA-sinA)(secA-cosA)=(1/sinA-sinA)(1/cosA-cosA)

=(1-sin²A/sinA)(1-cos²A/cosA)=cos²A/sinA *sin²A/cosA=sinAcosA

LHS:1/(tanA+CotA)=1/(sinA/cosA +cosA/sinA)=1/(cos²A+Sin²A/cosAsinA)=1/1/(cosAsinA)=cosAsinA=RHS

now sinAcosA = √2/4 =>( sinA./cosA)*cos A*cosA = √2/4=> tanA.cos²A = √2/4 => tanA/(sec²A) = √2/4=> tanA/(1+tan²A) = √2/4

Given,tan A = root(2) - 1

Then,tan A/ 1 + tan^2 A

= root(2) - 1/ 1 + [root(2) - 1]^2

= root(2) - 1/ (1 + 2 +1 - 2root(2))

= (root(2) - 1) / (4 - 2root(2))= root(2)[1 - 1/root(2)]/ 4[1 - 2root(2)/4]

= root(2)[1 - 1/root(2)]/ 4[1 - 1/root(2)]

= root(2)/4

Hence proved

√(sec theta- tan theta)²/sec²theta- tan²theta√(sectheta- tantheta)²sec theta- tan thetaas sec²theta-tan²theta=1

RHS = 1/cos theta- sin theeta/costhetasec theta- tan thetaLHS = RHS

Let the number be x

As per given conditionx + 5 = 17x = 17 - 5 = 12

Therefore, Number is 12

17-5=12 is right answer

it is right

of course it must be.

The unit is square yards

what the answer

yes

can i see the answer

ab*b - bc*c - ab + c*c = b(ab - c*c) - 1(ab - c*c) = (b-1)(ab-c*c)

ans in short

The formula of curved surface area of right circular cone is : pi*r*l

where r is the radius of and l is the slant height.

or

S = pi*x*(root(a^2 + x^2)

Solve for differentiation of S and equate it to zero since curved surface area is given as minimum.

that is dS/dx = 0

111/11=( 100+1)/(10+1)= 10.09Please like the solution 👍 ✔️

The number 5 added to three times the product of m and n is written as 3mn + 5.

sorry

i had to write something else

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the answer for the above question is pictograph

pictograph is the answer

pictograph is correct answer.

pictograph is the correct answer

the pictorial representation of data is called a pictograph

the pictorial representation of data is called a pictographs

(e) - (ii) pictograph

2)pictographs is the best answer

Let us assumeJacob’s current age is x his son’s current age is y

Five years hence, Jacob’s age = x + 5 his son’s age = y + 5

As per question;x + 5 = 3(y + 5)x + 5 = 3y + 15x = 3y + 15 – 5 = 3y + 10

Five years ago, Jacob’s age = x – 5 his son’s age = y – 5

As per question;x – 5 = 7(y – 5)x – 5 = 7y – 35x = 7y – 35 + 5 = 7y – 30

Substituting the value of x from first equation in this equation, we get3y + 10 = 7y – 303y + 10 + 30 = 7y7y – 3y = 404y = 40y = 10

Substituting the value of y in first equation, we getx = 3y + 10x = 3 x 10 + 10 = 40

Hence, Jacob’s age = 40 years and son’s age = 10 years

A circular flower bed is surrounding by a path 5m wide

the diameter of flower bed is 65mso, radius of circular flower bed = diameter/2 = 65/2 = 32.5m

area of circular bed = π × (32.5)² = 1056.25π m²

radius of circular bed + path = 32.5 + 5 = 37.5 m

Area of circular bed + path = π × (37.5)² = 1406.25π m²

Area of path = Area of (circular bed + path) + area of circular bed = 1406.25π - 1056.25π = 350 m²

answer=4/(a-b)right ans like this

4/(a-b). is very very right answer

4/(a-b) is correct answer.

2(x/a) + y/b = 2.....(1)x/a - y/b = 4...........(2)

Add eq(1) and eq(2)

3x/a = 6x = 6a/3 = 2a

Put value of x in eq(2)2a/a - y/b = 4y/b = 2 - 4y = - 2b

(B) is correct option

so much thank you sir it mean me alot

H = height of the cone , R = radius of the coneh = height of the cylinder, r = radius of the cylinder,S = lateral surface area of the cylinder

S = 2π r hr = R (1 - h/H) .

S = 2π (R (1 - h/H)) hdS/dh = 2π (R/H) (H - 2h)d²S/dh² = -4π (R/H)H - 2h = 0 .......... set dS/dh = 0 to find the stationary pointsh = H/2 .............. as d²S/dh² < 0

r = R (1 - (H/2)/H) ....... plug h=H/2 into r = R (1 - h/H)r = R/2

15+14=29

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From second equation,y=-3x=y x=-3

(a+b)(a-b)=a^2-b^2(2x+1/3y)(2x-1/3y)=4x^2-1/9y^26(-1/2)=4x^2-1/9y^24x^2-1/9y^2=-3

Circumference = 2 × pi × r 77 = 2 × 22/7 × r r = 7×77/44 Area = pi × r × r = 22/7 × 7×77/44 × 7×77/44 = 41503/88

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