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Question

Find out the value of sec15


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Solution

Step 1: Convert it into cosine form

Firstly, we will find the value of cos15°.

cos15°=cos(45°-30°)By using the formula,

cos(a-b)=cosacosb+sinasinb

Here,

a=45°and b=30°

cos15°=cos45°cos30°+sin45°sin30°

Step 2: Finding the value in cosine form and then converting it into secant.

cos15=12×32+12×12cos15=322+122cos15=3+122

Therefore,

sec15=1cos15sec15=13+122sec15=223+1

Hence,sec15=223+1


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