Advertisements
Advertisements
प्रश्न
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
विकल्प
- \[\frac{\pi}{6}\]
- \[\frac{\pi}{3}\]
- \[\frac{\pi}{4}\]
- \[\frac{\pi}{12}\]
Advertisements
उत्तर
60⁰ = \[\frac{\pi}{3}\]
Hence, `tan p=4sqrt3,tanQ=(3sqrt3)/14`
`cos(P-Q)= cosP cosQ+sinP sinQ`
`=1/7xx13/14+(4sqrt3)/7xx(3sqrt3)/14`
`=(13+36)/98`
`=49/98`
`thereforecos(P-Q)=1/2`
`=>P-Q=cos^(-1) 1/2`
`=>P-Q=60^circ`
Hence, the correct answer is option B.
APPEARS IN
संबंधित प्रश्न
Prove that `2 sin^2 pi/6 + cosec^2 (7pi)/6 cos^2 pi/3 = 3/2`
Prove that: `2 sin^2 (3pi)/4 + 2 cos^2 pi/4 + 2 sec^2 pi/3 = 10`
Prove the following:
`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`
Prove the following:
cos2 2x – cos2 6x = sin 4x sin 8x
Prove the following:
`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`
Prove the following:
`(sin x + sin 3x)/(cos x + cos 3x) = tan 2x`
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 36° cos 9° + cos 36° sin 9°
Prove that:
\[\frac{\tan \left( A + B \right)}{\cot \left( A - B \right)} = \frac{\tan^2 A - \tan^2 B}{1 - \tan^2 A \tan^2 B}\]
Prove that:
tan 8x − tan 6x − tan 2x = tan 8x tan 6x tan 2x
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
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:
\[\frac{1}{\sin \left( x - a \right) \sin \left( x - b \right)} = \frac{\cot \left( x - a \right) - \cot \left( x - b \right)}{\sin \left( a - b \right)}\]
Prove that:
If \[\tan\theta = \frac{\sin\alpha - \cos\alpha}{\sin\alpha + \cos\alpha}\] , then show that \[\sin\alpha + \cos\alpha = \sqrt{2}\cos\theta\].
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 tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B.
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 \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.
If A + B = C, then write the value of tan A tan B tan C.
The value of \[\sin^2 \frac{5\pi}{12} - \sin^2 \frac{\pi}{12}\]
If A + B + C = π, then sec A (cos B cos C − sin B sin C) is equal to
If in ∆ABC, tan A + tan B + tan C = 6, then cot A cot B cot C =
If \[\tan\theta = \frac{1}{2}\] and \[\tan\phi = \frac{1}{3}\], then the value of \[\tan\phi = \frac{1}{3}\] is
If tan (π/4 + x) + tan (π/4 − x) = a, then tan2 (π/4 + x) + tan2 (π/4 − x) =
Express the following as the sum or difference of sines and cosines:
2 cos 7x cos 3x
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 find the general value of θ.
If f(x) = cos2x + sec2x, then ______.
[Hint: A.M ≥ G.M.]
If tanα = `m/(m + 1)`, tanβ = `1/(2m + 1)`, then α + β is equal to ______.
If sinx + cosx = a, then |sinx – cosx| = ______.
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 cosecx = 1 + cotx then x = 2nπ, 2nπ + `pi/2`
In the following match each item given under the column C1 to its correct answer given under the column C2:
| Column A | Column B |
| (a) sin(x + y) sin(x – y) | (i) cos2x – sin2y |
| (b) cos (x + y) cos (x – y) | (ii) `(1 - tan theta)/(1 + tan theta)` |
| (c) `cot(pi/4 + theta)` | (iii) `(1 + tan theta)/(1 - tan theta)` |
| (d) `tan(pi/4 + theta)` | (iv) sin2x – sin2y |
