Question
Which of the following options is equal to tan A1−cot A+cot A1−tan A ?
Answer: Option A
:
A and B
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A and B
tan A1−cot A+cot A1−tan A
=tan A1−(1tan A)+1tan A1−tan A
=tan Atan A−1tan A+1tan A(1−tan A)
=tan2 Atan A−1−1tan A(tan A−1)……(a−b=−(b−a))
=tan3 A−1tan A(tan A−1)
=(/tan A−1)(tan2 A+tan A+1)tan A(/tan A−1)……[a3−b3=(a−b)(a2+ab+b2)]
=tan2 Atan A+tan Atan A+1tan A
=tan A + 1 + cot A
=1+sin AcosA+cos AsinA
=1+(sin2 A+cos2 Asin A cos A)
=1+1sin A cos A
=1+cosec A sec A
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