Question

Sintita/1-costita+sintita/1+costita=4 then find the value of tita​

Answer 1

Step-by-step explanation:

Given:-

[Sin θ/(1-Cos θ) ]+ [Sin θ/(1+Cos θ)] = 4

To find:-

Find the value of θ ?

Solution:-

Given that

[Sin θ/(1-Cos θ) ]+ [Sin θ/(1+Cos θ)] = 4

=> Sin θ [1 / (1-Cos θ)] + [1 / ( 1+ Cos θ)] = 4

=> Sinθ[{(1+Cos θ)+(1-Cosθ)}]/[(1-Cosθ)(1+Cosθ)=4

=>Sinθ [ (1+Cosθ+1-Cos θ)]/[(1)^2-(Cos θ)^2]=4

(Since (a+b)(a-b)=a^2-b^2))

=>Sin θ [(1+1)/(1-Cos^2 θ) = 4

=>Sin θ (2 / (1-Cos^2 θ) = 4

We know that

Sin^2 A + Cos^2 A = 1

=>Sin^2 A = 1 - Cos^2 A

=>Sin θ (2/Sin^2 θ) = 4

=> 2 Sin θ / (Sin θ × Sin θ) = 4

=> 2 / Sin θ = 4

=> 1/ Sin θ = 4/2

=> 1/ Sin θ = 2

=> Sin θ = 1/2

=> Sin θ = Sin 30°

=> θ = 30°

Therefore, θ = 30°

Answer:-

The value of θ for the given problem is 30°

Used formulae:-

• (a+b)(a-b)=a^2-b^2

• Sin^2 A + Cos^2 A = 1

• Sin 30° = 1/2