Question

cos thieta = 1\2 is true when sin thieta . cos thieta =​

Answer 1

Answer:

(1+sin

2

θ)=3sinθcosθ

⇒2+2sin

2

θ=3×2sinθcosθ

⇒2+1−cos2θ=3sin2θ

⇒3−cos2θ=3sin2θ

⇒3−

1+tan

2

θ

1−tan

2

θ

=3×

1+tan

2

θ

2tanθ

⇒

1+tan

2

θ

3+3tan

2

θ+1−tan

2

θ

=

1+tan

2

θ

6tanθ

⇒3+3tan

2

θ+1−tan

2

θ=6tanθ

⇒4+2tan

2

θ−6tanθ=0

⇒2tan

2

θ−6tanθ+4=0

⇒tan

2

θ−3tanθ+2=0

⇒(tanθ−1)(2tanθ−1)=0

⇒tanθ=1 or

2

1

Hence the given statement is false.