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SSC CGL 2022 PYQ — Question 61

SSC CGL - 02 Dec 2022 - Shift 1 • Quantitative Aptitude • Q61

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 If sin (A + B) = cos (A + B), what is the value of tan A?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 1−tanB1+tanB{1 -{tanB} \over 1+tanB}

Formula used:

sin (A + B) = sin A cos B + cos A sin B         ---- (1)

cos (A + B) = cos A cos B - sin A sin B           ---- (2)

Calculations:

According to the question;

⇒ sin (A + B) = cos (A + B)

Using equation (1) and (2), we get

⇒ sin A cos B + cos A sin B = cos A cos B - sin A sin B

⇒ sin A cos B + sin A sin B = cos A cos B - cos A sin B

⇒ sin A(cos B + sin B) = cos A (cos B - sin B)

⇒ sin A/cos A = (cos B - sin B)/(cos B + sin B)

⇒ tan A = (1 - tan B)/(1 + tan B)