Trigonometry Trouble

Geometry Level 1

If X is any angle and SinX +CosX =1, then what is SinX × CosX?


The answer is 0.

Parth Dwivedi by Parth Dwivedi , 26, India

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2 solutions

Nikhil Raj
Jun 6, 2017

sin ⁡ x + cos ⁡ x = 1 ( sin ⁡ x + cos ⁡ x ) 2 = 1 sin ⁡ 2 x + cos ⁡ 2 x + 2 sin ⁡ x cos ⁡ x = 1 1 + 2 sin ⁡ x cos ⁡ x = 1 2 sin ⁡ x cos ⁡ x = 0 sin ⁡ x cos ⁡ x = 0 \sin x + \cos x = 1 \\ (\sin x + \cos x)^2 = 1 \\ \sin^2 x + \cos^2x + 2\sin x\cos x = 1 \\ 1 + 2\sin x\cos x = 1 \\ 2\sin x\cos x = 0 \\ \sin x\cos x = \boxed{0}

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Yaten Sharma
Sep 7, 2014

Given is sinx + cosx =1 Squaring both sides we get 2sinxcosx = 0 hence sinx * cosx =0

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