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Assertion : sin cos67 67 12 2+ =c cReason : For any value of , sin cos 12 2θ θ θ+ =(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).(c) Assertion (A) is true but reason (R) is false.(d) Assertion (A) is false but reason (R) is true.

Question

Assertion : sin cos67 67 12 2+ =c cReason : For any value of , sin cos 12 2θ θ θ+ =(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).(c) Assertion (A) is true but reason (R) is false.(d) Assertion (A) is false but reason (R) is true.

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Solution

The assertion is false, but the reason is true. The assertion is incorrect because sin(67) + cos(67) does not equal 12/2. However, the reason is true in the sense that for any value of θ, sin^2(θ) + cos^2(θ) equals 1, not 12/2. Therefore, the correct answer is (d) Assertion (A) is false but reason (R) is true.

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