Question

please answer the following questions​

Answer 1

Answer:

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Answer 2

Solution

Given :-

• tan θ/tan (90° - θ) + sin(90° - θ)/cos θ = ..?

• (1 -cos A )(1 +sec A)/ tan A = ...?

Find :-

• These above Values.

Explanation

Take First.

= tan θ/tan (90° - θ) + sin(90° - θ)/cos θ

We Know,

• tan ( 90° - θ ) = cot θ
• sin ( 90° - θ ) = cos θ

So,

= tan θ /cot θ + cos θ/cos θ

= tan θ /cot θ + 1

= sin θ / cos θ × sin θ / cos θ + 1

= sin² θ / cos² θ + 1

= ( sin² θ + cos² θ )/cos² θ

= 1/cos² θ

= sec² θ

Since

• Your option will be (C). sec² θ .

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Take Second

= (1 -cos A )(1 +sec A)/ tan A

= ( 1 + sec A - cos A - cos A . sec A)/ tan A

= ( 1 + sec A - cos A - 1 )/ tan A

= (sec A - cos A)/tan A

= sec A/tan A - cos A/tan A

= (cos A /sinA ) × 1/cos A - cos A/sinA × cos A

= 1/sin A - cos² A/sin A

= (1 - cos² A)/sin A

= (sin² A) /sin A

= sin A

Hence

• Your Answer will be option number A. sin A

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