Advertisements
Advertisements
प्रश्न
If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B.
उत्तर
\[\tan 2B = \tan(B + B)\]
\[ = \tan(A + B - (A - B))\]
\[ = \frac{\tan(A + B) - \tan(A - B)}{1 + \tan(A + B)\tan(A - B)} \]
\[ = \frac{p - q}{1 + pq} \left[ \because \tan(A + B) = p \text{ and } \tan(A - B) = q \right]\]
APPEARS IN
संबंधित प्रश्न
Find the value of: sin 75°
Find the value of: tan 15°
Prove the following:
`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`
Prove the following:
`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`
Prove the following:
`(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x`
Prove the following:
cos 4x = 1 – 8sin2 x cos2 x
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:
sin (A + B)
Evaluate the following:
cos 47° cos 13° − sin 47° sin 13°
Prove that:
Prove that:
\[\cos^2 45^\circ - \sin^2 15^\circ = \frac{\sqrt{3}}{4}\]
Prove that:
sin2 (n + 1) A − sin2 nA = sin (2n + 1) A sin A.
Prove that:
Prove that:
tan 36° + tan 9° + tan 36° tan 9° = 1
Prove that:
tan 13x − tan 9x − tan 4x = tan 13x tan 9x tan 4x
If x lies in the first quadrant and \[\cos x = \frac{8}{17}\], then prove that:
If sin α + sin β = a and cos α + cos β = b, show that
Reduce each of the following expressions to the sine and cosine of a single expression:
24 cos x + 7 sin x
Show that sin 100° − sin 10° is positive.
If x cos θ = y cos \[\left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)\]then write the value of \[\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\]
If \[\frac{\cos \left( x - y \right)}{\cos \left( x + y \right)} = \frac{m}{n}\] then write the value of tan x tan y.
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 \[\cos P = \frac{1}{7}\text{ and }\cos Q = \frac{13}{14}\], where P and Q both are acute angles. Then, the value of P − Q is
The value of cos (36° − A) cos (36° + A) + cos (54° + A) cos (54° − A) is
If tan (π/4 + x) + tan (π/4 − x) = a, then tan2 (π/4 + x) + tan2 (π/4 − x) =
If cos (A − B) \[= \frac{3}{5}\] and tan A tan B = 2, then
If tan 69° + tan 66° − tan 69° tan 66° = 2k, then k =
Express the following as the sum or difference of sines and cosines:
2 sin 3x cos x
Match each item given under column C1 to its correct answer given under column C2.
| C1 | C2 |
| (a) `(1 - cosx)/sinx` | (i) `cot^2 x/2` |
| (b) `(1 + cosx)/(1 - cosx)` | (ii) `cot x/2` |
| (c) `(1 + cosx)/sinx` | (iii) `|cos x + sin x|` |
| (d) `sqrt(1 + sin 2x)` | (iv) `tan x/2` |
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 + cosecθ = 2, then sin2θ + cosec2θ is equal to ______.
The value of sin(45° + θ) - cos(45° - θ) is ______.
The value of `cot(pi/4 + theta)cot(pi/4 - theta)` is ______.
If α + β = `pi/4`, then the value of (1 + tan α)(1 + tan β) is ______.
If sinx + cosx = a, then |sinx – cosx| = ______.
3(sinx – cosx)4 + 6(sinx + cosx)2 + 4(sin6x + cos6x) = ______.
Given x > 0, the values of f(x) = `-3cos sqrt(3 + x + x^2)` lie in the interval ______.
State whether the statement is True or False? Also give justification.
If tanA = `(1 - cos B)/sinB`, then tan2A = tanB
