Question

(sec^2theta-1) (1-cosec^2theta)​

Answer 1

Step-by-step explanation:

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Answer 2

Given :

• $\sf{( \sec^{2} \theta - 1)( \csc^{2} \theta - 1)}$

Let us start the solution by solving with the LHS first.

$\implies{ \sf{( { \sec }^{2} \theta - 1)( \csc^{2} \theta - 1)}}$

$\dag{ \: \: \: \: \: \: \: \: \: \: \boxed{ \sf{1 + { \tan}^{2} \theta = \sec^{2} \theta}}}$

So from this identity, we can write $\sf{ { \sec}^{2} \theta}$ as

$\implies{ \sf{ { \sec}^{2} \theta = 1 + { \tan}^{2} \theta}}$

$\dag{ \: \: \: \: \: \: \: \: \: \boxed{ \sf{1 + { \cot}^{2} \theta = \csc^{2} \theta}}}$

From this identity, we can write $\sf{ \csc^{2} \theta}$ as

$\implies{ \sf{ { \csc }^{2} \theta = 1 + { \cot }^{2} \theta}}$

Substituting these both values,

$\implies{ \sf{ { \tan }^{2} \theta \times { \cot}^{2} \theta}}$

$\implies{ \sf{( \tan{ \theta} \times \cot{ \theta})^{2} }}$

We know that both tan and cot are reciprocals of each other.

So,

$\implies{ \sf{ \tan{ \theta} \times \cot{ \theta} = 1}}$

$\sf{ = 1}$ (RHS)

Hence, LHS = RHS.

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You must be thinking ye question maine solve kaise kiya hai? xD xD

Just learn the identities & learn substitution, aa jayega ._.

Have a G'day! ;)