Advertisements
Advertisements
प्रश्न
Prove that
Advertisements
उत्तर
\[\text{ LHS }= \frac{\cos8^\circ - \sin8^\circ}{\cos8^\circ + \sin8^\circ}\]
\[ = \frac{\frac{\cos8^\circ}{\cos8^\circ} - \frac{\sin8^\circ}{\cos8^\circ}}{\frac{\cos8}{\cos8} + \frac{\sin8}{\cos8}} \left( \text{ Dividing numeraor and denominator by }\cos 8^\circ \right)\]
\[ = \frac{1 - \tan8^\circ}{1 + \tan8^\circ}\]
\[ = \frac{1 - \tan8^\circ}{1 + 1 \times \tan8^\circ}\]
\[ = \frac{\tan45^\circ - \tan8^\circ}{1 + \tan45^\circ \tan8^\circ} \left( \text{ As }\tan 45^\circ = 1 \right)\]
\[ = \tan\left( 45^\circ - 8^\circ \right) \left[\text{ As }\frac{\tan A - \tan B}{1 + \tan A \tan B} = \tan\left( A + B \right) \right]\]
\[ = \tan37^\circ\]
= RHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
Prove that `2 sin^2 pi/6 + cosec^2 (7pi)/6 cos^2 pi/3 = 3/2`
Find the value of: sin 75°
Find the value of: tan 15°
Prove the following:
`(cos9x - cos5x)/(sin17x - sin 3x) = - (sin2x)/(cos 10x)`
Prove the following:
`(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x`
Prove the following:
cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1
Prove the following:
cos 4x = 1 – 8sin2 x cos2 x
If \[\sin A = \frac{1}{2}, \cos B = \frac{12}{13}\], where \[\frac{\pi}{2}\]< A < π and \[\frac{3\pi}{2}\] < B < 2π, find tan (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:
sin (A + B)
Prove that \[\frac{\tan 69^\circ + \tan 66^\circ}{1 - \tan 69^\circ \tan 66^\circ} = - 1\].
Prove that:
\[\cos^2 45^\circ - \sin^2 15^\circ = \frac{\sqrt{3}}{4}\]
Prove that: \[\frac{\sin \left( A + B \right) + \sin \left( A - B \right)}{\cos \left( A + B \right) + \cos \left( A - B \right)} = \tan A\]
Prove that:
\[\frac{\sin \left( A - B \right)}{\cos A \cos B} + \frac{\sin \left( B - C \right)}{\cos B \cos C} + \frac{\sin \left( C - A \right)}{\cos C \cos A} = 0\]
Prove that:
Prove that:
tan 8x − tan 6x − tan 2x = tan 8x tan 6x tan 2x
If tan (A + B) = x and tan (A − B) = y, find the values of tan 2A and tan 2B.
If α, β are two different values of x lying between 0 and 2π, which satisfy the equation 6 cos x + 8 sin x = 9, find the value of sin (α + β).
Prove that:
\[\frac{1}{\sin \left( x - a \right) \sin \left( x - b \right)} = \frac{\cot \left( x - a \right) - \cot \left( x - b \right)}{\sin \left( a - b \right)}\]
Prove that:
Show that sin 100° − sin 10° is positive.
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.
Write the interval in which the value of 5 cos x + 3 cos \[\left( x + \frac{\pi}{3} \right) + 3\] lies.
If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B.
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 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =
tan 3A − tan 2A − tan A =
The value of \[\cos^2 \left( \frac{\pi}{6} + x \right) - \sin^2 \left( \frac{\pi}{6} - x \right)\] 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
If `(sin(x + y))/(sin(x - y)) = (a + b)/(a - b)`, then show that `tanx/tany = a/b` [Hint: Use Componendo and Dividendo].
If sinθ + cosθ = 1, then the value of sin2θ is equal to ______.
The maximum distance of a point on the graph of the function y = `sqrt(3)` sinx + cosx from x-axis is ______.
State whether the statement is True or False? Also give justification.
If tanθ + tan2θ + `sqrt(3)` tanθ tan2θ = `sqrt(3)`, then θ = `("n"pi)/3 + pi/9`
