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 principal and general solutions of the equation `cot x = -sqrt3`
If \[\tan x = \frac{b}{a}\] , then find the values of \[\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}}\].
If \[T_n = \sin^n x + \cos^n x\], prove that \[\frac{T_3 - T_5}{T_1} = \frac{T_5 - T_7}{T_3}\]
Prove that: cos 24° + cos 55° + cos 125° + cos 204° + cos 300° = \[\frac{1}{2}\]
In a ∆ABC, prove that:
cos (A + B) + cos C = 0
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:
\[\sin\frac{13\pi}{3}\sin\frac{8\pi}{3} + \cos\frac{2\pi}{3}\sin\frac{5\pi}{6} = \frac{1}{2}\]
Prove that:
\[\sin \frac{13\pi}{3}\sin\frac{2\pi}{3} + \cos\frac{4\pi}{3}\sin\frac{13\pi}{6} = \frac{1}{2}\]
If \[\frac{\pi}{2} < x < \frac{3\pi}{2},\text{ then }\sqrt{\frac{1 - \sin x}{1 + \sin x}}\] is equal to
If tan \[x = - \frac{1}{\sqrt{5}}\] and θ lies in the IV quadrant, then the value of cos x is
If \[cosec x - \cot x = \frac{1}{2}, 0 < x < \frac{\pi}{2},\]
If tan A + cot A = 4, then tan4 A + cot4 A is equal to
If sec x + tan x = k, cos x =
Which of the following is correct?
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:
`cosec x = 1 + cot x`
Solve the following equation:
4sinx cosx + 2 sin x + 2 cosx + 1 = 0
Solve the following equation:
\[2^{\sin^2 x} + 2^{\cos^2 x} = 2\sqrt{2}\]
Write the number of solutions of the equation
\[4 \sin x - 3 \cos x = 7\]
Write the values of x in [0, π] for which \[\sin 2x, \frac{1}{2}\]
and cos 2x are in A.P.
Write the number of points of intersection of the curves
Write the solution set of the equation
The number of solution in [0, π/2] of the equation \[\cos 3x \tan 5x = \sin 7x\] is
In (0, π), the number of solutions of the equation \[\tan x + \tan 2x + \tan 3x = \tan x \tan 2x \tan 3x\] is
The number of values of x in [0, 2π] that satisfy the equation \[\sin^2 x - \cos x = \frac{1}{4}\]
General solution of \[\tan 5 x = \cot 2 x\] is
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
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°
2 sin2x + 1 = 3 sin x
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ * tan 130^circ)` =
Solve the equation sin θ + sin 3θ + sin 5θ = 0
Solve `sqrt(3)` cos θ + sin θ = `sqrt(2)`
If a cosθ + b sinθ = m and a sinθ - b cosθ = n, then show that a2 + b2 = m2 + n2
