Cos minus theta is equal to cos theta: Proof

Cos minus theta is equal to cos theta, that is, cos(-θ) = cosθ. Similarly, cos(-x) = cosx. In this post, we learn to find the value of cos of minus theta.

The cos minus theta formula is given as follows: cos(-θ) = cosθ.

Prove that cos(-theta) = cos theta

We will follow the below steps to compute cos(-theta).

Step 1:

Write -θ = 0-θ

Step 2:

Applying the formula cos(a-b) = cosa cosb + sina sinb with a=0 and b=θ, we obtain that

cos(-θ) = cos(0-θ)

= cos0 cosθ +sin0 sinθ

= 1 × cosθ + 0 × sinθ

= cosθ + 0

= cosθ.

That is, cos(-θ) = cosθ.

So the value of cos(-θ) is equal to cosθ.

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Question-Answer

Question: Find the value of cos(-45°).

Answer:

By the above formula cos(-θ) = cosθ with θ=45°, we get that

cos(-45°) = cos45° = 1/√2.

So the value of cos minus 45 degree is equal to 1/√2.

Also Read: sin3x formula in terms of sinx

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