Question

how to solve for x if Sin(x-20)= Cos(3x+10)

Answer 1

Step-by-step explanation:

sin(x−20

∘

)=cos(3x−10

∘

)

⇒sin(x−20

∘

)=sin(90

∘

−(3x−10

∘

)) since sin(90

∘

−θ)=cosθ

⇒x−20

∘

=90

∘

−(3x−10

∘

)

⇒x−20

∘

=90

∘

−3x+10

∘

⇒x+3x=100

∘

+20

∘

=120

∘

⇒4x=120

∘

∴x=

4

120

∘

=30

∘

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

• sin(x - 20) = cos(3x + 10)

To Find:

• Value of x

Solution:

⇒ sin(x - 20) = cos(3x + 10)

We know that,

cos(a) = sin(90-a)

⇒ sin(x - 20) = sin(90 - (3x + 10))

⇒ sin(x - 20) = sin(90 - 3x - 10)

⇒ sin(x - 20) = sin(80 - 3x)

So,

⇒ x - 20 = 80 - 3x

⇒ x + 3x = 80 + 20

⇒ 4x = 100

⇒ x = 25