1.

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Answer»

Given :-

4tan∅ = 3

tan∅ = 3/4

Method 1 :-

You can SOLVE further by taking ∅ = 37°.

sin 37° = 3/5

cos 37° = 4/5

( 4*(3/5) - (4/5) + 1 )

———————————

( 4*(4/5) + (4/5) - 1 )

( (8/5) + 1 )

——————

( 4 - 1 )

( 13/5)

———

3

13/15

Method 2 :-

CALCULATE sin∅ and cos∅ by FORMING a right angled triangle with PERPENDICULAR 3 and base as 4.

sin∅ = 3/5

cos∅ = 4/5

Putting values in Original Question :-

( 4sin∅ - cos∅ + 1 )

———————————

( 4sin∅ + cos∅ - 1 )

( 4*(3/5) - (4/5) + 1 )

———————————

( 4*(4/5) + (4/5) - 1 )

( (8/5) + 1 )

——————

( 4 - 1 )

( 13/5)

———

3

13/15

Method 3 :-

Simplify it in tan∅ and sec∅ and then use

1 + tan²∅ = sec²∅

ANSWER

So, answer of this question is 13/15

Thank you.

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