Advertisements
Advertisements
प्रश्न
sin6 A + cos6 A + 3 sin2 A cos2 A =
विकल्प
0
1
2
3
Advertisements
उत्तर
1
We have:
\[ \sin^6 A + \cos^6 A + 3\left( \sin^2 A \right) \left( \cos^2 A \right)\]
\[ = \left( \sin^2 A \right)^3 + \left( \cos^2 A \right)^3 + 3\left( \sin^2 A \right) \left( \cos^2 A \right) \times 1\]
\[ = \left( \sin^2 A \right)^3 + \left( \cos^2 A \right)^3 + 3\left( \sin^2 A \right) \left( \cos^2 A \right)\left( \sin^2 A + \cos^2 A \right)\]
\[ = \left( \sin^2 A + \cos^2 A \right)^3 \]
\[ = 1^3 = 1\]
APPEARS IN
संबंधित प्रश्न
Find the principal and general solutions of the equation sec x = 2
Find the general solution of cosec x = –2
Find the general solution of the equation sin x + sin 3x + sin 5x = 0
If \[\tan x = \frac{a}{b},\] show that
If \[a = \sec x - \tan x \text{ and }b = cosec x + \cot x\], then shown that \[ab + a - b + 1 = 0\]
Prove that:
\[\sec\left( \frac{3\pi}{2} - x \right)\sec\left( x - \frac{5\pi}{2} \right) + \tan\left( \frac{5\pi}{2} + x \right)\tan\left( x - \frac{3\pi}{2} \right) = - 1 .\]
In a ∆ABC, prove that:
In a ∆A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that cos(180° − A) + cos (180° + B) + cos (180° + C) − sin (90° + D) = 0
If \[0 < x < \frac{\pi}{2}\], and if \[\frac{y + 1}{1 - y} = \sqrt{\frac{1 + \sin x}{1 - \sin x}}\], then y is equal to
If \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] is equal to
If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
If \[\frac{3\pi}{4} < \alpha < \pi, \text{ then }\sqrt{2\cot \alpha + \frac{1}{\sin^2 \alpha}}\] is equal to
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
sin2 π/18 + sin2 π/9 + sin2 7π/18 + sin2 4π/9 =
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
Which of the following is incorrect?
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:
Solve the following equation:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0
Solve the following equation:
3tanx + cot x = 5 cosec x
Solve the following equation:
3sin2x – 5 sin x cos x + 8 cos2 x = 2
Write the number of solutions of the equation tan x + sec x = 2 cos x in the interval [0, 2π].
If a is any real number, the number of roots of \[\cot x - \tan x = a\] in the first quadrant is (are).
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
The solution of the equation \[\cos^2 x + \sin x + 1 = 0\] lies in the interval
If \[\cos x = - \frac{1}{2}\] and 0 < x < 2\pi, then the solutions are
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`
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
Solve the equation sin θ + sin 3θ + sin 5θ = 0
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
