Question

if 10 theta = 1/ root 7
show that cosec ² theta - sec ²theta
upon cosec²theta + sec²theta =3/4​

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

If tan θ = , Show that

★═════════════════★

♣ ᴀɴꜱᴡᴇʀ :

We know :

So comparing this formula and value of tan θ from question, we get :

Height = 1

Base = √7

Now we need to Prove the value of :

Also :

From this we get :

But we have Height and Base, we dont have Hypotenuse.

Hypotenuse can be found by using Pythagoras Theorem

Pythagoras Theorem states that :

Hypotenuse² = Side² + Side²

For our question :

Hypotenuse² = Height² + Base²

Hypotenuse² = 1² + √7²

Hypotenuse² = 1 + 7

Hypotenuse² = 8

√Hypotenuse² = √8

Hypotenuse = √8

➢ Let's find value's of cosec²θ and sec²θ

________________________________________

First cosec²θ :

cosec²θ = 8

________________________________________

Now sec²θ :

sec²θ = 8/7

________________________________________

Now Proving :

Taking L.H.S :

= R.H.S

Hence Proved !!!

Answer 2

$\large\mapsto\boxed{ \sf \green{Answer :) }} \:$

$\purple{ \mathsf{first \: refer \: to \: the \: attachment}}$

$\pink{ \mathtt{ so \: \frac{3}{4} is \: your \: answer \: mate}}$