Question

Prove that sin(30+theta) + cos(60+theta) = costheta

Answer 1

Answer:

sin(30+@)+cos(60+@)

sin30.cos@+cos30.sin@[email protected]@

1/2cos@+√3/2sin@+1/2cos @-√3/2sin@

1/2cos@+1/2cos@

cos@

prove that

Answer 2

Given:

• sin(30°+θ)+cos(60°+θ) = cosθ

To Find:

• To Prove that,  sin(30°+θ)+cos(60°+θ) = cosθ

Solution:

• Consider LHS = sin(30°+θ)+cos(60°+θ)  → (1) and RHS = cosθ
• We have standard trigonometry formula saying,
• sin(A+B) = sinAcosB+cosAsinB and cos(A+B) = cosAcosB - sinAsinB
• The mentioned formula can be applied for equation (1)
• We get, RHS = sin30°cosθ + cos30°sinθ + cos60°cosθ - sin60°sinθ
• RHS = $\frac{1}{2}$ cosθ + $\frac{\sqrt{3} }{2}$sinθ + $\frac{1}{2}$cosθ - $\frac{\sqrt{3} }{2}$sinθ = cosθ = RHS
• LHS = RHS

Hence Proved

sin(30°+θ)+cos(60°+θ) = cosθ