Advertisements
Advertisements
प्रश्न
If tan θ1 tan θ2 = k, then \[\frac{\cos \left( \theta_1 - \theta_2 \right)}{\cos \left( \theta_1 + \theta_2 \right)} =\]
विकल्प
- \[\frac{1 + k}{1 - k}\]
- \[\frac{1 - k}{1 + k}\]
- \[\frac{k + 1}{k - 1}\]
- \[\frac{k - 1}{k + 1}\]
Advertisements
उत्तर
\[\frac{\cos( \theta_1 - \theta_2 )}{\cos( \theta_1 + \theta_2 )}\]
\[ = \frac{\cos \theta_1 \cos \theta_2 + \sin \theta_1 \sin \theta_2}{\cos \theta_1 \cos \theta_2 - \sin \theta_1 \sin \theta_2}\]
\[\text{ Dividing numerator and denominator by }\cos \theta_1 \cos \theta_2 ,\text{ we get }:\]
\[\frac{1 + \tan \theta_1 \tan \theta_2}{1 - \tan \theta_1 \tan \theta_2}\]
\[ = \frac{1 + k}{1 - k}\]
APPEARS IN
संबंधित प्रश्न
Prove the following:
`cos ((3pi)/ 2 + x ) cos(2pi + x) [cot ((3pi)/2 - x) + cot (2pi + x)]= 1`
Prove the following:
`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`
Prove the following:
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Prove the following:
`(sin x - siny)/(cos x + cos y)= tan (x -y)/2`
Prove the following:
cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1
Prove that: `(cos x + cos y)^2 + (sin x - sin y )^2 = 4 cos^2 (x + y)/2`
Prove that: sin 3x + sin 2x – sin x = 4sin x `cos x/2 cos (3x)/2`
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 \[\tan A = \frac{3}{4}, \cos B = \frac{9}{41}\], where π < A < \[\frac{3\pi}{2}\] and 0 < B <\[\frac{\pi}{2}\], find tan (A + B).
If \[\sin A = \frac{1}{2}, \cos B = \frac{\sqrt{3}}{2}\], where \[\frac{\pi}{2}\] < A < π and 0 < B < \[\frac{\pi}{2}\], find the following:
tan (A - B)
Evaluate the following:
sin 78° cos 18° − cos 78° sin 18°
Evaluate the following:
cos 80° cos 20° + sin 80° sin 20°
Prove that
\[\frac{\tan A + \tan B}{\tan A - \tan B} = \frac{\sin \left( A + B \right)}{\sin \left( A - B \right)}\]
Prove that
Prove that:
Prove that \[\frac{\tan 69^\circ + \tan 66^\circ}{1 - \tan 69^\circ \tan 66^\circ} = - 1\].
Prove that:
\[\frac{\tan^2 2x - \tan^2 x}{1 - \tan^2 2x \tan^2 x} = \tan 3x \tan x\]
If tan (A + B) = x and tan (A − B) = y, find the values of tan 2A and tan 2B.
If x lies in the first quadrant and \[\cos x = \frac{8}{17}\], then prove that:
If sin (α + β) = 1 and sin (α − β) \[= \frac{1}{2}\], where 0 ≤ α, \[\beta \leq \frac{\pi}{2}\], then find the values of tan (α + 2β) and tan (2α + β).
Prove that:
\[\frac{1}{\sin \left( x - a \right) \sin \left( x - b \right)} = \frac{\cot \left( x - a \right) - \cot \left( x - b \right)}{\sin \left( a - b \right)}\]
If sin α sin β − cos α cos β + 1 = 0, prove that 1 + cot α tan β = 0.
Reduce each of the following expressions to the sine and cosine of a single expression:
cos x − sin x
Show that sin 100° − sin 10° is positive.
Prove that \[\left( 2\sqrt{3} + 3 \right) \sin x + 2\sqrt{3} \cos x\] lies between \[- \left( 2\sqrt{3} + \sqrt{15} \right) \text{ and } \left( 2\sqrt{3} + \sqrt{15} \right)\]
If α + β − γ = π and sin2 α +sin2 β − sin2 γ = λ sin α sin β cos γ, then write the value of λ.
If A + B = C, then write the value of tan A tan B tan C.
tan 20° + tan 40° + \[\sqrt{3}\] tan 20° tan 40° is equal to
If A + B + C = π, then \[\frac{\tan A + \tan B + \tan C}{\tan A \tan B \tan C}\] is equal to
The value of \[\cos^2 \left( \frac{\pi}{6} + x \right) - \sin^2 \left( \frac{\pi}{6} - x \right)\] is
If cos (A − B) \[= \frac{3}{5}\] and tan A tan B = 2, then
If 3 tan (θ – 15°) = tan (θ + 15°), 0° < θ < 90°, then θ = ______.
If cotθ + tanθ = 2cosecθ, then find the general value of θ.
The value of tan3A - tan2A - tanA is equal to ______.
If tanα = `1/7`, tanβ = `1/3`, then cos2α is equal to ______.
If tanθ = `a/b`, then bcos2θ + asin2θ is equal to ______.
If sinx + cosx = a, then sin6x + cos6x = ______.
Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval ______.
