Question

sec^2 x-1/tan^2x = 1



Please help

Answer 1

$\large{\underbrace{\underline{\sf{Understanding\; the\; Concept}}}}$

Here in this question, concept of trigonometric Identities is used. We have to prove LHS=RHS. We can prove it simply by following steps.

So let's start!!

$\rule{250}{2}$

We have Identity:

1+tan²∅=sec²∅

By transporting LHS and RHS, we get:

tan²∅=sec²∅-1....(1)

We have to proof:-

$\Large\sf\implies \dfrac{\sec^2x-1}{\tan^2x}=1$

So let's take LHS

$\Large\sf\implies LHS=\dfrac{\sec^2x-1}{\tan^2x}$

By putting value of sec²x from equation (1)

$\Large\sf\implies LHS=\dfrac{\tan^2x}{\tan^2x}$

Cancelling same denominator and numerator

$\Large{\sf{\implies LHS=1}}$

$\large{\sf \implies RHS=1}$

★ LHS=RHS

$\Large\underline{\boxed{\sf{\red{Hence\; Proved}}}}$

$\rule{250}{2}$

Learn More Identities!!

• 1+cot²∅=cosec²∅

• cosec²∅-cot²∅=1

• cot²∅-cosec²∅=-1

• sin²∅+cos²∅=1

• sin²∅=1-cos²∅

• cos²∅=1-sin²∅