SSC CGL 23 Aug 2021 Shift 2 Paper

Question : 74 of 100

Marks: +1, -0

(cosec A-\cot A)(1+\cos A)=?

Solution:

(cosec A-\cot A)(1+\cos A)

\;\; =(\;{1}/{\sin A}-\;{\cos A}/{\sin A}) ×(1+\cos A)

\;\; =\;{(1-\cos A)}/{\sin A} ×(1+\cos A)

\;\; =\;{1-\cos ^{2} A}/{\sin A} \;\; [ ∵ (a+b)(a-b)=a^{2}-b^{2}]

\;\; =\;{\sin ^{2} A}/{\sin A} \;\; [ ∵ 1-\cos ^{2} θ=\sin ^{2} θ]

\;\; =\sin A

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