Question

Heres the question

Class 10 Trigonometry ​

Answer 1

Step-by-step explanation:

Let theta = x

According to the given question,

• cosec^2x . tan^x - 1 = tan^2x

L.H.S.

• cosec^2x . tan^2x - 1

We know, cosec^2x = 1+cot^2x

Putting the values we get,

• (1+cot^2x)tan^2x - 1

• tan^2x +cot^2x.tan^2x - 1

• As cotx.tanx = 1

So, cot^2x.tan^2x also = 1

• tan^2x +1-1

• tan^2x R.H.S. proved.

Answer 2

Solution :-

We have to show

cosec²∅tan²∅ - 1 = tan²∅

Now by solving LHS Further :-

As cosec∅ = 1/sin∅

and tan∅ = sin∅/cos∅

$\rightarrow \dfrac{1}{sin^2\theta} \times \dfrac{sin^2\theta}{cos^2\theta} - 1$

$\rightarrow \dfrac{1}{cos^2\theta} - 1$

$\rightarrow \dfrac{1 - cos^2\theta}{cos^2\theta}$

Now as sin²∅ + cos²∅ = 1

→ 1 - cos²∅ = sin²∅

$\rightarrow \dfrac{sin^2\theta}{cos^2\theta}$

$\rightarrow tan^2\theta$

Now our LHS = tan²∅

And RHS = tan²∅

→ LHS = RHS

Hence Shown.