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vaieri [72.5K]
2 years ago
9

Establish the identity. (2 cos 0-6 sin 0)² + (6 cos 0+2 sin 0)2 = 40

Mathematics
1 answer:
kogti [31]2 years ago
8 0

Rewriting the left-hand side as follows,

(2\cos\theta-6\sin \theta)^2 +(6\cos \theta+2\sin \theta)^2\\\\=4\cos^2 \theta-24\cos \theta \sin \theta+36 \sin^2 \theta+36 \cos^2 \theta+24 \cos \theta \sin \theta+4 \sin^2 \theta\\\\=40\cos^2 \theta+40 \sin^2 \theta\\\\=40(\cos^2 \theta+\sin^2 \theta)\\\\=40

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2) Simplify 7 × 2 to 14 .

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3) Simplify 14 + 1 to 15.

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