Question

if teta and 2 teta -45 are acute angles such that sin teta =cos (2 teta -45),then tan teta is equal to​

Answer 1

Answer:

sin7θ=cos2θ

∴sin7θ=sin(90

∘

−2θ)

⇒7θ=90

∘

−2θ

⇒7θ+2θ=90

∘

⇒9θ=90

∘

⇒θ=10

∘

Now,2sin3θ−

3

tan3θ=2sin3×10

∘

−

3

tan310

∘

=2sin30

∘

−

3

tan30

∘

=2×

2

1

−

3

×

3

1

=1−1=0

Answer 2

Answer:

sin7θ=cos2θ

∴sin7θ=sin(90

∘

−2θ)

⇒7θ=90

∘

−2θ

⇒7θ+2θ=90

∘

⇒9θ=90

∘

⇒θ=10

∘

Now,2sin3θ−

3

tan3θ=2sin3×10

∘

−

3

tan310

∘

=2sin30

∘

−

3

tan30

∘

=2×

2

1

−

3

×

3

1

=1−1=0