Advertisements
Advertisements
प्रश्न
If \[f\left( x \right) = \cos^2 x + \sec^2 x\], then
विकल्प
f(x) < 1
f(x) = 1
1 < f(x) < 2
f(x) ≥ 2
Advertisements
उत्तर
\[f\left( x \right) = \cos^2 x + \sec^2 x\]
\[ = \cos^2 x + \sec^2 x - 2\cos x\sec x + 2\cos x\sec x\]
\[ = \left( \sec x - \cos x \right)^2 + 2\]
\[ \therefore f\left( x \right) \geq 2 \forall x \left[ \left( \sec x - \cos x \right)^2 \geq 0 \forall x \right]\]
Hence, the correct option is answer f(x) ≥ 2.
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation `tan x = sqrt3`
Find the general solution of the equation cos 4 x = cos 2 x
Find the general solution for each of the following equations sec2 2x = 1– tan 2x
If \[\sin x + \cos x = m\], then prove that \[\sin^6 x + \cos^6 x = \frac{4 - 3 \left( m^2 - 1 \right)^2}{4}\], where \[m^2 \leq 2\]
Prove that: tan 225° cot 405° + tan 765° cot 675° = 0
Prove that:
\[\frac{\cos (2\pi + x) cosec (2\pi + x) \tan (\pi/2 + x)}{\sec(\pi/2 + x)\cos x \cot(\pi + x)} = 1\]
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
Prove that:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
Find the general solution of the following equation:
Find the general solution of the following equation:
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]
If secx cos5x + 1 = 0, where \[0 < x \leq \frac{\pi}{2}\], find the value of x.
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
Write the general solutions of tan2 2x = 1.
Write the set of values of a for which the equation
Write the number of points of intersection of the curves
Write the number of values of x in [0, 2π] that satisfy the equation \[\sin x - \cos x = \frac{1}{4}\].
If \[3\tan\left( x - 15^\circ \right) = \tan\left( x + 15^\circ \right)\] \[0 < x < 90^\circ\], find θ.
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
A solution of the equation \[\cos^2 x + \sin x + 1 = 0\], lies in the interval
If \[4 \sin^2 x = 1\], then the values of x are
General solution of \[\tan 5 x = \cot 2 x\] is
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin θ + cos θ = `sqrt(2)`
Solve the following equations:
cot θ + cosec θ = `sqrt(3)`
Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)
Choose the correct alternative:
If tan α and tan β are the roots of x2 + ax + b = 0 then `(sin(alpha + beta))/(sin alpha sin beta)` is equal to
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
