Advertisements
Advertisements
प्रश्न
Evaluate the following:
cos 80° cos 20° + sin 80° sin 20°
Advertisements
उत्तर
\[\cos80^\circ\cos20^\circ + \sin80^\circ \sin20^\circ\]
\[ = \cos\left( 80^\circ - 20^\circ \right) \left[\text{ Using }\cos A \cos B + \sin A \sin B = \cos\left( A - B \right) \right]\]
\[ = \cos60^\circ = \frac{1}{2}\]
APPEARS IN
संबंधित प्रश्न
Find the value of: tan 15°
Prove the following:
sin2 6x – sin2 4x = sin 2x sin 10x
Prove the following:
cos 4x = 1 – 8sin2 x cos2 x
Prove that: `(cos x - cosy)^2 + (sin x - sin y)^2 = 4 sin^2 (x - y)/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:
sin (A − B)
If \[\sin A = \frac{12}{13}\text{ and } \sin B = \frac{4}{5}\], where \[\frac{\pi}{2}\] < A < π and 0 < B < \[\frac{\pi}{2}\], find the following:
sin (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:
sin 36° cos 9° + cos 36° sin 9°
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:
\[\frac{7\pi}{12} + \cos\frac{\pi}{12} = \sin\frac{5\pi}{12} - \sin\frac{\pi}{12}\]
Prove that:
cos2 A + cos2 B − 2 cos A cos B cos (A + B) = sin2 (A + B)
Prove that:
tan 13x − tan 9x − tan 4x = tan 13x tan 9x tan 4x
If tan A = x tan B, prove that
\[\frac{\sin \left( A - B \right)}{\sin \left( A + B \right)} = \frac{x - 1}{x + 1}\]
If tan (A + B) = x and tan (A − B) = y, find the values of tan 2A and tan 2B.
If sin α + sin β = a and cos α + cos β = b, show that
Find the maximum and minimum values of each of the following trigonometrical expression:
12 cos x + 5 sin x + 4
Find the maximum and minimum values of each of the following trigonometrical expression:
\[5 \cos x + 3 \sin \left( \frac{\pi}{6} - x \right) + 4\]
Find the maximum and minimum values of each of the following trigonometrical expression:
sin x − cos x + 1
Write the maximum value of 12 sin x − 9 sin2 x.
If 12 sin x − 9sin2 x attains its maximum value at x = α, then write the value of sin α.
If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B.
If A + B + C = π, then \[\frac{\tan A + \tan B + \tan C}{\tan A \tan B \tan C}\] is equal to
If cot (α + β) = 0, sin (α + 2β) is equal to
If \[\tan\theta = \frac{1}{2}\] and \[\tan\phi = \frac{1}{3}\], then the value of \[\tan\phi = \frac{1}{3}\] 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 = ______.
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 cotθ + tanθ = 2cosecθ, then find the general value of θ.
If tanα = `m/(m + 1)`, tanβ = `1/(2m + 1)`, then α + β 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 tanα = `1/7`, tanβ = `1/3`, then cos2α is equal to ______.
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 |
