SSC Selection Post 2022 PYQ — Question 73

SSC Selection Post - Higher Secondary Level 2022 - 11 Feb 2022 - Shift 1 • Quantitative Aptitude • Q73

In △ABC, right-angled at B, if tan A = 121 \over 2, then the value of sinA(cosA−cosC)cosC(sinc−sinA)sinA(cosA - cosC) \over cosC(sin c - sin A) is:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 1.

tan A = 121 \over 2 = PBP\over B

H2 = B2 + P2

H = 5\sqrt5

here, H  = Hypotaneous, B = Base, P = Perpendicular

sinA(cosA−cosC)cosC(sinc−sinA)sinA(cosA - cosC) \over cosC(sin c - sin A)

⇒ 15(25−15)15(25−15){1\over \sqrt5}({2\over \sqrt5} - {1\over \sqrt5}) \over {1\over \sqrt5}({2\over \sqrt5} -{1\over \sqrt5}) 

⇒ 15×1515×15{1\over \sqrt5} \times {1\over \sqrt5}\over {1\over \sqrt5} \times {1\over \sqrt5} = 1