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Chapter 7: Q. 40 (page 501)

Establish the identity.

sin鈦�(伪)鈭�sin鈦�(尾)cos鈦�(伪)鈭�cos鈦�(尾)

Short Answer

Expert verified

鈭�cot鈦�伪+尾2

Step by step solution

01

Step 1. Given information

We have been givensin鈦�(伪)鈭�sin鈦�(尾)cos鈦�(伪)鈭�cos鈦�(尾).

We have to establish identity.

02

Step 2. Solve for the numerator part first

Numerator of the given expression has the formsin伪-sin尾

Therefore, we get

role="math" sin伪-sin尾=2sin鈦�伪-尾2cos鈦�伪+尾2

03

Step 3. Solve for the denominator part

Denominator of the given expression has the formcos伪-cos尾

Therefore, we get

cos伪-cos尾=鈭�2sin鈦�伪+尾2sin鈦�伪鈭�尾2

04

Step 4. Plug the above result

Plug the above results in the expression:

sin鈦�(伪)鈭�sin鈦�(尾)cos鈦�(伪)鈭�cos鈦�(尾)=2sin鈦�伪鈭�尾2cos鈦�伪+尾2鈭�2sin鈦�伪+尾2sin鈦�伪鈭�尾2=鈭�cos鈦�伪+尾2sin鈦�伪+尾2=鈭�cot鈦�伪+尾2

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