JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1

The most general value of

\theta

for which

\sin \,\,\theta - \cos \,\,\theta = \mathop {\min }\limits_{x\; \in \;R} \,\,\left\{ {1,\;\,{x^2} - 4x + 6} \right\}

are given by

View answer and explanation

Correct option: B

\theta = n\pi \,\, + \,\,{\left( { - 1} \right)^n}\frac{\pi }{4}\,\, + \,\,\frac{\pi }{4},\,\,n \in Z

Option B (

\theta = n\pi \\ + \\ {\left( { - 1} \right)^n}\frac{\pi }{4}\\ + \\ \frac{\pi }{4},\n \in Z

) is correct because it is the general solution of the trigonometric equation after finding the minimum value of the quadratic expression.

More Questions from TRIGONOMETRIC EQUATIONS

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\sin \,\,x\,\,\;cos\,\,3x = \sin \,\,3x\,\,\cos \,\,5x

\left[ {0,\;\,\frac{\pi }{2}} \right]

\left( {x,\,y} \right)

x,\,\,y \in \left[ {0,10} \right]

\left( {\sqrt {{{\sin }^2} - \sin \,\,x + \frac{1}{2}} } \right){2^{{{\sec }^2}y}}\,\, \cdot \,\, \le 1

\mathrm{X}

\theta \rightarrow \frac{\pi}{2}

\sin x+\cos x=\frac{\sqrt{7}}{2}

x \in\left[0, \frac{\pi}{4}\right]

\tan \frac{x}{2}

\tan \frac{\pi}{5}+2 \tan \frac{2 \pi}{5}+4 \cot \frac{4 \pi}{5}

0 < x < \pi

\cos x+\sin x=\frac{1}{2}

\tan x