Advertisements
Advertisements
प्रश्न
If tan 69° + tan 66° − tan 69° tan 66° = 2k, then k =
विकल्प
−1
- \[\frac{1}{2}\]
- \[- \frac{1}{2}\]
None of these
Advertisements
उत्तर
\[\tan135^\circ = \tan(90^\circ + 45^\circ)\]
\[ = - \tan45^\circ\]
\[ = - 1\]
\[Or, \tan(69^\circ + 66^\circ) = \frac{\tan69^\circ + \tan66^\circ}{1 - \tan69^\circ \tan66^\circ}\]
\[ \Rightarrow - 1 = \frac{\tan69^\circ + \tan66^\circ}{1 - \tan69^\circ \tan66^\circ}\]
\[ \Rightarrow \tan69^\circ + \tan66^\circ - \tan69^\circ\tan66^\circ = - 1\]
Therefore,
\[2k = - 1\]
\[ \Rightarrow k = \frac{- 1}{2}\]
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: `(tan(pi/4 + x))/(tan(pi/4 - x)) = ((1+ tan x)/(1- tan x))^2`
Prove the following:
`cos ((3pi)/ 2 + x ) cos(2pi + x) [cot ((3pi)/2 - x) + cot (2pi + x)]= 1`
Prove the following:
`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`
Prove the following:
sin2 6x – sin2 4x = sin 2x sin 10x
Prove the following:
cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x)
Prove the following:
`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`
Prove the following:
`(sin x - siny)/(cos x + cos y)= tan (x -y)/2`
Prove that: sin 3x + sin 2x – sin x = 4sin x `cos x/2 cos (3x)/2`
Prove that
Prove that
Prove that:
If \[\tan A = \frac{m}{m - 1}\text{ and }\tan B = \frac{1}{2m - 1}\], then prove that \[A - B = \frac{\pi}{4}\].
Prove that:
\[\cos^2 45^\circ - \sin^2 15^\circ = \frac{\sqrt{3}}{4}\]
Prove that:
cos2 A + cos2 B − 2 cos A cos B cos (A + B) = sin2 (A + B)
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 13x − tan 9x − tan 4x = tan 13x tan 9x tan 4x
Prove that:
\[\frac{\tan^2 2x - \tan^2 x}{1 - \tan^2 2x \tan^2 x} = \tan 3x \tan x\]
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).
If sin α + sin β = a and cos α + cos β = b, show that
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 a = b \[\cos \frac{2\pi}{3} = c \cos\frac{4\pi}{3}\] then write the value of ab + bc + ca.
The value of \[\sin^2 \frac{5\pi}{12} - \sin^2 \frac{\pi}{12}\]
If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =
If in ∆ABC, tan A + tan B + tan C = 6, then cot A cot B cot C =
The value of cos (36° − A) cos (36° + A) + cos (54° + A) cos (54° − A) is
If \[\tan\alpha = \frac{x}{x + 1}\] and \[\tan\alpha = \frac{x}{x + 1}\], then \[\alpha + \beta\] is equal to
Express the following as the sum or difference of sines and cosines:
2 cos 3x sin 2xa
Show that 2 sin2β + 4 cos (α + β) sin α sin β + cos 2(α + β) = cos 2α
Find the general solution of the equation `(sqrt(3) - 1) costheta + (sqrt(3) + 1) sin theta` = 2
[Hint: Put `sqrt(3) - 1` = r sinα, `sqrt(3) + 1` = r cosα which gives tanα = `tan(pi/4 - pi/6)` α = `pi/12`]
The value of tan 75° - cot 75° is equal to ______.
If tanα = `m/(m + 1)`, tanβ = `1/(2m + 1)`, then α + β is equal to ______.
If tanα = `1/7`, tanβ = `1/3`, then cos2α 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`
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 |
