How to solve these trigonometric equations?

Question

Please show step by step how you solved the value of theta :)

1. cos²Ө = 1 - 2sin²Ө

2. 2(sec²Ө + tan²Ө) = 11

Answer 1

1. cos²Ө = 1 - 2sin²Ө
 

Recall Pythagorean identity: sin² θ + cos² θ = 1 ---->  cos² θ = 1-sin²θ

1-sin²Ө = 1 - 2sin²Ө

sin²Ө=0

sinӨ=0

Ө=nπ

Where n=0,1,2,3...............

2. 2(sec²Ө + tan²Ө) = 11

Recall trignometric identity: sec² θ - tan² θ = 1 ---->  1 + tan² θ = sec²θ

2(1 + tan² θ + tan²Ө) = 11

(1 +2 tan² θ) = 11/2

2 tan² θ=9/2

tan² θ=9/4

tanθ=3/2

Using calculator

θ=56.3

I hope it helps!!!

 

 

Comments

You are correct...
1
cos²Ө = 1 - 2sin²Ө
Ө=nπ, where n is the set of integers.