Question

$\large{\texttt{\purple{Prove \: That : - }}}$
Cosec 2A - Cot 2A = Tan A

Best Of Luck❤️​

Answer 1

Given:

• Cosec 2A - Cot 2A = Tan A

To Find

• Prove cosec 2A - cot 2A = tan A?

Solution

${\tt\purple{ Cosec \ 2A - cot \ 2A = tan \ A }} \\ \\ \\ \colon\implies{\tt{ Cosec \ 2A - cot \ 2A = \dfrac{1}{sin \ 2A} - \dfrac{cos \ 2A}{sin \ 2A} }} \\ \\ \\ \colon\implies{\tt{ \dfrac{1 - cos \ 2A}{sin \ 2A} }} \\ \\ \\ \colon\implies{\tt{ \dfrac{2 \ sin^2 A}{2 \ sin \ A \ cos \ A } }} \\ \\ \\ \colon\implies{\tt{ \dfrac{sin \ A}{cos \ A} }} \\ \\ \\ \colon\implies{\boxed{\tt\green{ tan \ A }}}$

Hence Proved..!!!

More to Know

• Trigonometry is the branch of mathematics which deals with the study of properties of triangles (sides and angles).
• cos $\theta$ . sec $\theta$ = 1
• cos $\theta$ = 1/sec $\theta$
• cosec $\theta$ = 1/sin $\theta$
• sin $\theta$ = 1/Cosec $\theta$