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Question

cosec15°-sec15° is equal to


A

22

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B

6

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C

26

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D

6+2

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Solution

The correct option is A

22


Explanation for the correct option:

Step 1. Given cosec15°sec15°

=1sin15°1cos15°

=(cos15°sin15°)(sin15°cos15°)

Step 2. Multiply and divide it by 2,

=2(cos15°sin15°)(2sin15°cos15°)

=2(cos15°sin15°)sin30° ; 2sinθcosθ=sin2θ

Step 3. Multiply and divide it by 2,

=2cosec30°×2×12cos15°12sin15°

=2×2×2×[sin45°cos15°cos45°sin15°] ; cosec30°=2,sin45°=12,cos45°=-12

=42[sin(45°15°)] sinAcosB-cosAsinB=sin(A-B)

=42sin30°

=42×12

=22

Hence, Option ‘A’ is Correct.


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