Question

(1+cot^2 a)*tan a/sec^2 a=cot a

Answer 1

(1+cot^2 A)*tan A/sec^2 A

we know that (cosecx)^2-(cotx)^2=1

=》1+(cotx)^2=(cosecx)^2

(1+cot^2 A)*tan A/sec^2 A

=((cosecA)^2)(tanA)/((secA)^2)

=((cosA)^2/(sinA)^2)(sinA/cosA)

=cosA/sinA

=cotA

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Answer 2

$\frac{(1 + {cot}^{2}a)tana }{ {sec}^{2} a} \\ \\ = \frac{ {cosec}^{2}atana }{ {sec}^{2} a} \\ \\ = \frac{1}{ {sin}^{2}a } . \frac{sina}{cosa} . {cos}^{2} a \\ \\ = \frac{cosa}{sina} \\ \\ = cota$