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Chapter 7: Q. 15 (page 485)

Find the exact value of the expression:

cos165鈭�

Short Answer

Expert verified

鈭�14(6+2)

Step by step solution

01

Step 1. Given information 

We have been given an expression cos165鈭�.

We have to find its exact value.

02

Step 2. Simplify the expression

We can also write the expression as:

cos165鈭�=cos(135鈭�+30掳)

03

Step 3.  Apply the compound angle formula

cos(135鈭�+30掳)has the form of cos(伪+尾)

Therefore, apply

cos伪+尾=cos伪cos尾-sin伪sin尾

cos鈦�135鈭�cos鈦�30鈭�鈭�sin鈦�135鈭�sin鈦�30鈭�=鈭�22鈰�32鈭�22鈰�12=鈭�64鈭�24=鈭�6鈭�24=鈭�14(6+2)

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