Question

prove:
tan A+ cot A = sec A cosec A
​

Answer 1

Answer:

sin A/cos A + cosA/sinA

= (sin^2 A + cos^2A)/ sinA cos A

= 1/sinA cos A

sec A cosec A

Answer 2

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\red{\underline \bold{To \: Prove : }} \\ \tt: \implies tan \: A+ cot \: A = sec \:A \: cosec \: A$

• According to given question :

$\tt: \implies tan \: A+ cot \: A= sec \: A \: cosec \: A \\ \\ \bold{Solving \: L.H.S } \\ \tt: \implies tan \: A+ cot \: A\\ \\ \tt \circ \: tan \: A= \frac{sin \: A}{cos \: A} \\ \\ \tt: \implies \frac{sin \: A}{cos \: A} + cot \: A\\ \\ \tt \circ \: cot \:A = \frac{cos \: A}{sin \: A } \\ \\ \tt: \implies \frac{sin \: A}{cos \: A} + \frac{cos \: A}{sin \: A} \\ \\ \tt: \implies \frac{sin \: A \times sin \: A + cos \: A \times cos \: A}{cos \: A \times sin \: A} \\ \\ \tt: \implies \frac{ {sin}^{2} \: A+ {cos}^{2} \: A }{cos \: \times sin \:A } \\ \\ \tt \circ \: {sin }^{2} \: A + {cos}^{2} \: A = 1 \\ \\ \tt: \implies \frac{1}{cos \: A\times sin \: A} \\ \\ \tt \circ \: cos \: A= \frac{1}{sec \: A} \\ \\ \tt \circ \: sin \: A= \frac{1}{cosec \: A} \\ \\ \tt: \implies \frac{1}{ \frac{1}{sec \: A \times cosec \: A} } \\ \\ \green{\tt: \implies sec \: A \: cosec \: A} \\ \\ \green{\tt \therefore L.H.S = R.H.S} \\ \\ \: \: \red{\huge{ \bold{Proved }}}$