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Chapter 7: Q. 24 (page 505)

use sum, difference, product, or half-angle formulas to find the exact value of each expression

cos65掳cos20掳+sin65掳sin20掳

Short Answer

Expert verified

cos65掳cos20掳+sin65掳sin20掳=12

Step by step solution

01

Step 1.Given Informatiion

cos65掳cos20掳+sin65掳sin20掳

02

Step 2. Using formula of (sin a + sin b )&(cos a +cos b)

We know :

cosacosb=12[cos(a+b)+cos(a-b)]sinasinb=-12[cos(a+b)-cos(a-b)]

Using it :

cos65掳cos20掳+sin65掳sin20掳=12[cos(65掳+20掳)+cos(65掳-20掳)]-12[cos(65掳+20掳)-cos(65掳-20掳)]cos65掳cos20掳+sin65掳sin20掳=12[cos85掳+cos45掳]-12[cos85掳-cos45掳]cos65掳cos20掳+sin65掳sin20掳=cos45掳cos65掳cos20掳+sin65掳sin20掳=12

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