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Question

2sin-135+cos-12425=


A

π2

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B

2π3

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C

5π3

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D

Noneofthese

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Solution

The correct option is A

π2


Explanation for the correct option:

Step 1. Solve the given expression:

2sin-135+cos-12425

=sin-12×35×1-352+cos-12425 2sin-1x=sin-1(2x1-x2)

=sin-12425+cos-12425

=cos-11-24252+cos-12425 sin-1x=cos-1(1-x2)

=cos-1725+cos-12425

Step 2. Apply formula cos-1x-cos-1y=xy+1-x2×1-y2

=cos-1725×2425+1-7252×1-24252

=cos-1725×2425149625×[1576625

=cos-1168625576625×49625

=cos-11686252425×725

=cos-1(0)

=cos-1cosπ2=π2 cos-1[x][-1,1]

Hence, Option ‘A’ is Correct.


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