Consider the triple ( ( x,

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Consider the triple (sin⁡x, cos⁡x, tan⁡x)=(−1213, 513, −125)\bigl(\sin x,\, \cos x,\, \tan x\bigr) = \left(-\dfrac{12}{13},\, \dfrac{5}{13},\, -\dfrac{12}{5}\right). Answer the following: (i) Verify whether sin⁡2x+cos⁡2x=1\sin^2 x + \cos^2 x = 1 for the given values. (ii) State the quadrant in which such an angle xx would lie, if it exists. (iii) Conclude whether the given triple can represent (sin⁡x,cos⁡x,tan⁡x)\bigl(\sin x, \cos x, \tan x\bigr) for some real angle xx. Justify briefly.

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