Advertisements
Advertisements
प्रश्न
Prove that
Advertisements
उत्तर
\[\text{ LHS }= \frac{\cos11^\circ + \sin11^\circ}{\cos11^\circ - \sin11^\circ}\]
\[ = \frac{\frac{\cos11^\circ}{\cos11^\circ} + \frac{\sin11^\circ}{\cos11^\circ}}{\frac{\cos11^\circ}{\cos11^\circ} - \frac{\sin11^\circ}{\cos11^\circ}} \left( \text{ Dividing numerator and denominator by }\cos11^\circ \right)\]
\[ = \frac{1 + \tan11^\circ}{1 - \tan11^\circ}\]
\[ = \frac{1 + \tan11^\circ}{1 - 1 \times \tan11^\circ}\]
\[ = \frac{\tan45^\circ + \tan11^\circ}{1 - \tan45^\circ \tan11^\circ} \left(\text{ As }\tan45^\circ = 1 \right)\]
\[ = \tan\left( 45^\circ + 11^\circ \right) \left[\text{ As }\frac{\tan A + \tan B}{1 - \tan A \tan B} = \tan\left( A + B \right) \right]\]
\[ = \tan56^\circ\]
= RHS
Hence proved .
APPEARS IN
संबंधित प्रश्न
Prove that `cot^2 pi/6 + cosec (5pi)/6 + 3 tan^2 pi/6 = 6`
Prove the following: `(tan(pi/4 + x))/(tan(pi/4 - x)) = ((1+ tan x)/(1- tan x))^2`
Prove the following:
`(cos (pi + x) cos (-x))/(sin(pi - x) cos (pi/2 + x)) = cot^2 x`
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:
sin (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).
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°
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
\[\frac{\tan A + \tan B}{\tan A - \tan B} = \frac{\sin \left( A + B \right)}{\sin \left( A - B \right)}\]
Prove that:
Prove that:
sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.
Prove that:
Prove that:
tan 8x − tan 6x − tan 2x = tan 8x tan 6x tan 2x
Prove that sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.
If sin α + sin β = a and cos α + cos β = b, show that
If sin α + sin β = a and cos α + cos β = b, show that
Prove that:
Find the maximum and minimum values of each of the following trigonometrical expression:
sin x − cos x + 1
Reduce each of the following expressions to the sine and cosine of a single expression:
\[\sqrt{3} \sin x - \cos x\]
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.
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 in ∆ABC, tan A + tan B + tan C = 6, then cot A cot B cot C =
tan 3A − tan 2A − tan A =
If cot (α + β) = 0, sin (α + 2β) is equal to
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 4x sin 3x
Show that 2 sin2β + 4 cos (α + β) sin α sin β + cos 2(α + β) = cos 2α
If sin(θ + α) = a and sin(θ + β) = b, then prove that cos 2(α - β) - 4ab cos(α - β) = 1 - 2a2 - 2b2
[Hint: Express cos(α - β) = cos((θ + α) - (θ + β))]
If f(x) = cos2x + sec2x, then ______.
[Hint: A.M ≥ G.M.]
The value of tan 75° - cot 75° is equal to ______.
If sinθ + cosθ = 1, then the value of sin2θ is equal to ______.
State whether the statement is True or False? Also give justification.
If cosecx = 1 + cotx then x = 2nπ, 2nπ + `pi/2`
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`
