Advertisements
Advertisements
प्रश्न
The value of sin25° + sin210° + sin215° + ... + sin285° + sin290° is
विकल्प
7
8
9.5
10
Advertisements
उत्तर
9.5
We have:
\[ \sin^2 5^\circ + \sin^2 10^\circ + \sin^2 15^\circ + . . . + \sin^2 85^\circ + \sin^2 90^\circ\]
\[ = \sin^2 5^\circ + \sin^2 10^\circ + \sin^2 15^\circ + . . . + \sin^2 \left( 90^\circ - 10^\circ \right) + \sin^2 \left( 90^\circ - 5^\circ \right) + \sin^2 90^\circ\]
\[ = \sin^2 5^\circ + \sin^2 10^\circ + \sin^2 15^\circ + . . . + \cos^2 10^\circ + \cos^2 5^\circ + \sin^2 90^\circ\]
\[ = \left( \sin^2 5^\circ + \cos^2 5^\circ \right) + \left( \sin^2 10^\circ + \cos^2 10^\circ \right) + + \left( \sin^2 15^\circ + \cos^2 15^\circ \right)\]
\[ + \left( \sin^2 20^\circ + \cos^2 20^\circ \right) + \left( \sin^2 25^\circ + \cos^2 25^\circ \right) + \left( \sin^2 30^\circ + \cos^2 30^\circ \right) \]
\[ + \left( \sin^2 35^\circ + \cos^2 35^\circ \right) + \left( \sin^2 40^\circ + \cos^2 40^\circ \right) + \sin^2 45^\circ + \sin^2 90^\circ\]
\[ = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + \left( \frac{1}{\sqrt{2}} \right)^2 + \left( 1 \right)^2 \left[ \because \sin^2 \theta + \cos^2 \theta = 1 \right]\]
\[ = 8 + \frac{1}{2} + 1\]
\[ = 9 . 5\]
APPEARS IN
संबंधित प्रश्न
Find the general solution of the equation sin 2x + cos x = 0
If \[\sin x = \frac{a^2 - b^2}{a^2 + b^2}\], then the values of tan x, sec x and cosec x
If \[T_n = \sin^n x + \cos^n x\], prove that \[6 T_{10} - 15 T_8 + 10 T_6 - 1 = 0\]
Prove that:
Prove that: \[\tan\frac{11\pi}{3} - 2\sin\frac{4\pi}{6} - \frac{3}{4} {cosec}^2 \frac{\pi}{4} + 4 \cos^2 \frac{17\pi}{6} = \frac{3 - 4\sqrt{3}}{2}\]
Prove that:
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
Find x from the following equations:
\[cosec\left( \frac{\pi}{2} + \theta \right) + x \cos \theta \cot\left( \frac{\pi}{2} + \theta \right) = \sin\left( \frac{\pi}{2} + \theta \right)\]
Find x from the following equations:
\[x \cot\left( \frac{\pi}{2} + \theta \right) + \tan\left( \frac{\pi}{2} + \theta \right)\sin \theta + cosec\left( \frac{\pi}{2} + \theta \right) = 0\]
Prove that:
\[\tan 4\pi - \cos\frac{3\pi}{2} - \sin\frac{5\pi}{6}\cos\frac{2\pi}{3} = \frac{1}{4}\]
Prove that:
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
sin6 A + cos6 A + 3 sin2 A cos2 A =
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
Find the general solution of the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
Solve the following equation:
\[2 \sin^2 x = 3\cos x, 0 \leq x \leq 2\pi\]
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 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.
If \[\tan px - \tan qx = 0\], then the values of θ form a series in
The general solution of the equation \[7 \cos^2 x + 3 \sin^2 x = 4\] is
The general value of x satisfying the equation
\[\sqrt{3} \sin x + \cos x = \sqrt{3}\]
A value of x satisfying \[\cos x + \sqrt{3} \sin x = 2\] is
If \[e^{\sin x} - e^{- \sin x} - 4 = 0\], then x =
Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`
Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
sin4x = sin2x
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
Solve the following equations:
sin θ + cos θ = `sqrt(2)`
Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = 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)
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then find the value of θ.
