Question

if sin theta = 1/2
show that:-
3 cos theta- 4 cos^2 theta​

Answer 1

Step-by-step explanation:

ANSWER

3sin θ+4cosθ = 5

Squaring both sides

9sin

2

θ+16cos

2

θ+24sinθcosθ=25

9(1 cos

2

=θ)+16(1−sinθ)+24sinθcosθ=25

9−9cos

2

θ+16−16sin

2

θ+24sinθcosθ=25

- 9 cos

2

θ−16sin

2

θ+24sinθcosθ=25916

9 cos

2

θ+16sin

2

θ−24sinθcosθ=0

(3cosθ4sinθ)

2

=0

3cosθ−4sinθ=0

Alternate Method:

If ax+by=m and ax−by=n

then (a

2

+b

2

)(x

2

+y

2

)=m

2

+n

2

Here

a=sinθ

x = 3, m = 5, and b = cos θ y = 4, n = ?

(sin

2

θ+cos

2

θ)(9+16)(5)

2

+n

2

n

2

= 0, n = 0

3sinθ−4cosθ = 0

Answer 2

Answer:

0

Step-by-step explanation:

Let theta be ₹.

sin ₹ = 1/2

sin ₹ = sin 30°

₹ = 30°

to prove:-

3cos₹ - 4cos^3₹ = 0

3cos30° - 4cos^3 30° = 0

3(root3/2)-4(root3-2)³=0

0 = 0