Trigonometry crush 2

Geometry Level 3

( cos ⁡ α + cos ⁡ β ) 2 + ( sin ⁡ α + sin ⁡ β ) 2 = p ⋅ cos ⁡ 2 ( α − β 2 ) \large ( \cos\alpha + \cos\beta)^2 + (\sin\alpha + \sin\beta)^2 = p \cdot \cos^2 \left( \frac{\alpha - \beta}2\right)

Above shows a trigonometric identity for all α \alpha and β \beta with constant p p . Find the value of p p .


The answer is 4.

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Raj Rajput by RAJ RAJPUT , 25, India

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2 solutions

Raj Rajput
Aug 7, 2015

7 Helpful 0 Interesting 0 Brilliant 0 Confused

I too did it in the same way. Can you tell me how did post this picture.

Utkarsh Kumar - 3 years, 4 months ago
Zahle Khan
Sep 2, 2015

Let alpha=A beta=B and A=B (since it is true for all values of x)

(2cosA)^2 + (2sinB)^2=p

4cos^2(A) + 4sin^2(B)=p

p=4

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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