Question

Class:- 10
Ch-> Intro to Trigonometry

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Answer 1

Step-by-step explanation:

Given :-

Sin θ = 5/13

To find :-

Find the value of

[(Cos²θ-Sin²θ)/(2SinθCosθ)] ×(1/Tan²θ) ?

Solution :-

Given that

Sinθ = 5/13

On squaring both sides then

=> Sin²θ = (5/13)²

=> Sin²θ = 25/169

On subtracting above from 1 both sides then

=> 1-Sin²θ = 1-(25/169)

=> Cos²θ = (169-25)/169

Since , Sin²θ + Cos²θ = 1

=> Cos²θ = 144/169

=> Cosθ = √(144/169)

=> Cosθ = 12/13

Now

We know that

Tanθ = Sinθ / Cosθ

=> Tanθ = (5/13)/(12/13)

=> Tanθ = (5/13)×(13/12)

=> Tanθ = 5/12

Now,

[(Cos²θ-Sin²θ)/(2SinθCosθ)] ×(1/Tan²θ)

=>[(12/13)²-(5/13)²]/(2(5/13)(12/13)]×[1/(5/12)²]

=>[{(144/169)-(25/169)}/(120/169)]

×[1/(25/144)]

=> [{(144-25)/169}/(120/169)]×(144/25)

=>[(119/169)/(120/169)] × (144/25)

=> [(119/169)×(169/120)]×(144/25)

=> (119/120)×(144/25)

=> (119×144)/(120×25)

=>17136/3000

=> 4284/750

=> 2142/375

=> 714/125

Answer:-

The required answer for the given problem is 714/125

Used formulae:-

→ Sin²θ + Cos²θ = 1

→ Tanθ = Sinθ / Cosθ