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 general solution of cosec x = –2
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
If \[cosec x - \sin x = a^3 , \sec x - \cos x = b^3\], then prove that \[a^2 b^2 \left( a^2 + b^2 \right) = 1\]
If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
Prove that:
\[\sin^2 \frac{\pi}{18} + \sin^2 \frac{\pi}{9} + \sin^2 \frac{7\pi}{18} + \sin^2 \frac{4\pi}{9} = 2\]
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:
cos (A + B) + cos C = 0
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
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 \[\frac{\pi}{2} < x < \pi, \text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}} + \sqrt{\frac{1 + \sin x}{1 - \sin x}}\] 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
If \[cosec x + \cot x = \frac{11}{2}\], then tan x =
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:
\[\sec x\cos5x + 1 = 0, 0 < x < \frac{\pi}{2}\]
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].
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
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
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
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 cos2x + 1 = – 3 cos x
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Solve the following equations:
cot θ + cosec θ = `sqrt(3)`
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
