Advertisements
Advertisements
प्रश्न
Write the maximum value of 12 sin x − 9 sin2 x.
Advertisements
उत्तर
\[\text{ Let } f\left( x \right) = 12\sin x - 9 \sin^2 x \]
\[ = - \left( 9 \sin^2 x - 12 \sin x \right) \]
\[ = - \left[ \left( 3\sin x \right)^2 - 2 . 3 \sin x . 2 + 2^2 - 4 \right]\]
\[ = - \left[ \left( 3 \sin x - 2 \right)^2 - 4 \right]\]
\[ = 4 - \left( 3 \sin x - 2 \right)^2 \]
\[\text{ Minimum value of } \left( 3 \sin x - 2 \right)^2 is 0 . \]
\[\text{ Therefore, maximum value of} 4 - \left( 3 \sin x - 2 \right)^2 \text{ would be } 4 .\]
APPEARS IN
संबंधित प्रश्न
Prove that `2 sin^2 pi/6 + cosec^2 (7pi)/6 cos^2 pi/3 = 3/2`
Prove that: `2 sin^2 (3pi)/4 + 2 cos^2 pi/4 + 2 sec^2 pi/3 = 10`
Find the value of: tan 15°
Prove the following:
`(cos (pi + x) cos (-x))/(sin(pi - x) cos (pi/2 + x)) = cot^2 x`
Prove the following:
`cos ((3pi)/ 2 + x ) cos(2pi + x) [cot ((3pi)/2 - x) + cot (2pi + x)]= 1`
Prove the following:
sin2 6x – sin2 4x = sin 2x sin 10x
Prove the following:
`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`
Prove the following:
`(sin x - siny)/(cos x + cos y)= tan (x -y)/2`
Prove that: sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x
Prove that: `((sin 7x + sin 5x) + (sin 9x + sin 3x))/((cos 7x + cos 5x) + (cos 9x + cos 3x)) = tan 6x`
If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the following:
If \[\sin A = \frac{4}{5}\] and \[\cos B = \frac{5}{13}\], where 0 < A, \[B < \frac{\pi}{2}\], find the value of the following:
cos (A + B)
If \[\sin A = \frac{12}{13}\text{ and } \sin B = \frac{4}{5}\], where \[\frac{\pi}{2}\] < A < π and 0 < B < \[\frac{\pi}{2}\], find the following:
cos (A + B)
If \[\cos A = - \frac{24}{25}\text{ and }\cos B = \frac{3}{5}\], where π < A < \[\frac{3\pi}{2}\text{ and }\frac{3\pi}{2}\]< B < 2π, find the following:
cos (A + B)
If \[\tan A = \frac{3}{4}, \cos B = \frac{9}{41}\], where π < A < \[\frac{3\pi}{2}\] and 0 < B <\[\frac{\pi}{2}\], find tan (A + B).
Evaluate the following:
cos 80° cos 20° + sin 80° sin 20°
Prove that
Prove that:
Prove that:
If \[\tan A = \frac{5}{6}\text{ and }\tan B = \frac{1}{11}\], prove that \[A + B = \frac{\pi}{4}\].
Prove that:
cos2 A + cos2 B − 2 cos A cos B cos (A + B) = sin2 (A + B)
If x lies in the first quadrant and \[\cos x = \frac{8}{17}\], then prove that:
Find the maximum and minimum values of each of the following trigonometrical expression:
12 sin x − 5 cos x
Find the maximum and minimum values of each of the following trigonometrical expression:
\[5 \cos x + 3 \sin \left( \frac{\pi}{6} - x \right) + 4\]
Find the maximum and minimum values of each of the following trigonometrical expression:
sin x − cos x + 1
If 12 sin x − 9sin2 x attains its maximum value at x = α, then write the value of sin α.
If a = b \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.
If \[\tan A = \frac{a}{a + 1}\text{ and } \tan B = \frac{1}{2a + 1}\]
tan 3A − tan 2A − tan A =
If tan (π/4 + x) + tan (π/4 − x) = a, then tan2 (π/4 + x) + tan2 (π/4 − x) =
The maximum value of \[\sin^2 \left( \frac{2\pi}{3} + x \right) + \sin^2 \left( \frac{2\pi}{3} - x \right)\] is
If tan 69° + tan 66° − tan 69° tan 66° = 2k, then k =
If sinθ + cosθ = 1, then find the general value of θ.
If tanα = `1/7`, tanβ = `1/3`, then cos2α is equal to ______.
If tanθ = `a/b`, then bcos2θ + asin2θ is equal to ______.
The maximum distance of a point on the graph of the function y = `sqrt(3)` sinx + cosx from x-axis is ______.
