Question

Prove that: cos130 cos 40+sin 130 sin 40 =0

Answer 1

you can see your answer

Answer 2

The proof is given below.

Given:

The expression cos130 cos 40+sin 130 sin40 = 0.

To Find:

The proof of the given expressions.

Solution:

To prove the given expression, cos130cos 40 + sin130sin40 = 0, we will use the below trigonometric identity involving the cosine of two different angles, say A and B.

cos(A - B) = cosAcos B + sinAsinB

Taking A = 130 and B = 40, The LHS of the given expression becomes,

cos130cos 40 + sin130sin40 = cos (130 - 40) = cos 90.

The value of cos 90 = 0.

⇒ The LHS and RHS of the given expressions are equal.

Hence proved.

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