Advertisements
Advertisements
प्रश्न
Prove that:
Advertisements
उत्तर
LHS = \[\sin\left( \frac{4\pi}{9} + 7 \right)\cos\left( \frac{\pi}{9} + 7 \right) - \cos\left( \frac{4\pi}{9} + 7 \right)\sin\left( \frac{\pi}{9} + 7 \right)\]
\[ = \sin\left[ \left( \frac{4\pi}{9} + 7 \right) - \left( \frac{\pi}{9} + 7 \right) \right] \left[ \sin A\cos B - \cos A\sin B = \sin\left( A - B \right) \right]\]
\[ = \sin\frac{3\pi}{9}\]
\[ = \sin\frac{\pi}{3}\]
\[ = \frac{\sqrt{3}}{2}\]
= RHS
APPEARS IN
संबंधित प्रश्न
Prove the following:
cos2 2x – cos2 6x = sin 4x sin 8x
Prove the following:
`(cos9x - cos5x)/(sin17x - sin 3x) = - (sin2x)/(cos 10x)`
Prove the following:
`(sin x - siny)/(cos x + cos y)= tan (x -y)/2`
Prove the following:
`(sin x + sin 3x)/(cos x + cos 3x) = tan 2x`
Prove the following:
cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1
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)
Evaluate the following:
cos 80° cos 20° + sin 80° sin 20°
If \[\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}\], where A lies in the second quadrant and B in the third quadrant, find the values of the following:
sin (A + B)
If \[\cos A = - \frac{12}{13}\text{ and }\cot B = \frac{24}{7}\], where A lies in the second quadrant and B in the third quadrant, find the values of the following:
cos (A + B)
Prove that
Prove that:
If \[\tan A = \frac{m}{m - 1}\text{ and }\tan B = \frac{1}{2m - 1}\], then prove that \[A - B = \frac{\pi}{4}\].
Prove that:
sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.
Prove that:
tan 8x − tan 6x − tan 2x = tan 8x tan 6x tan 2x
Prove that:
tan 13x − tan 9x − tan 4x = tan 13x tan 9x tan 4x
If sin α + sin β = a and cos α + cos β = b, show that
Prove that:
\[\frac{1}{\sin \left( x - a \right) \sin \left( x - b \right)} = \frac{\cot \left( x - a \right) - \cot \left( x - b \right)}{\sin \left( a - b \right)}\]
Find the maximum and minimum values of each of the following trigonometrical expression:
sin x − cos x + 1
Prove that \[\left( 2\sqrt{3} + 3 \right) \sin x + 2\sqrt{3} \cos x\] lies between \[- \left( 2\sqrt{3} + \sqrt{15} \right) \text{ and } \left( 2\sqrt{3} + \sqrt{15} \right)\]
Write the maximum and minimum values of 3 cos x + 4 sin x + 5.
Write the interval in which the value of 5 cos x + 3 cos \[\left( x + \frac{\pi}{3} \right) + 3\] lies.
If a = b \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.
If A + B = C, then write the value of tan A tan B tan C.
If tan \[\alpha = \frac{1}{1 + 2^{- x}}\] and \[\tan \beta = \frac{1}{1 + 2^{x + 1}}\] then write the value of α + β lying in the interval \[\left( 0, \frac{\pi}{2} \right)\]
If \[\cos P = \frac{1}{7}\text{ and }\cos Q = \frac{13}{14}\], where P and Q both are acute angles. Then, the value of P − Q is
If tan θ1 tan θ2 = k, then \[\frac{\cos \left( \theta_1 - \theta_2 \right)}{\cos \left( \theta_1 + \theta_2 \right)} =\]
If A − B = π/4, then (1 + tan A) (1 − tan B) is equal to
Express the following as the sum or difference of sines and cosines:
2 sin 3x cos x
Express the following as the sum or difference of sines and cosines:
2 sin 4x sin 3x
Show that 2 sin2β + 4 cos (α + β) sin α sin β + cos 2(α + β) = cos 2α
If cos(θ + Φ) = m cos(θ – Φ), then prove that 1 tan θ = `(1 - m)/(1 + m) cot phi`
[Hint: Express `(cos(theta + Φ))/(cos(theta - Φ)) = m/1` and apply Componendo and Dividendo]
If sinθ + cosecθ = 2, then sin2θ + cosec2θ is equal to ______.
If f(x) = cos2x + sec2x, then ______.
[Hint: A.M ≥ G.M.]
If sinθ + cosθ = 1, then the value of sin2θ is equal to ______.
If sinx + cosx = a, then sin6x + cos6x = ______.
