2cos(45°+Θ).cos(45°-Θ) = cos²Θ- sin²Θ | Prove | Trigonometric Ratios of Compound Angles | Trigonometry | Sci-Pi

Prove that:

2cos(45°+Θ).cos(45°-Θ) = cos²Θ- sin²Θ

 Answer:

You have two ways of bringing the conclusion. One is the way I solved this question and the other is to get cos2Θ as we know cos²Θ-sin²Θ = cos2Θ. But, solving it the way I solved, we need to first know the formula of Trigonometric Ratios of Compound Angles. You can see the following figure to know more about it.

So, if you understand these formulas and use your algebraic knowledge of Mathematics, you will be easily able to solve such questions in Trigonometry of Mathematics.

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