Advertisements
Advertisements
प्रश्न
Prove that:
tan 36° + tan 9° + tan 36° tan 9° = 1
Advertisements
उत्तर
\[\text{ We know that }36^\circ + 9^\circ = 45^\circ\]
Therefore,
\[ \tan\left( 36^\circ + 9^\circ \right) = \tan45^\circ\]
\[ \Rightarrow \frac{\tan36^\circ + \tan9^\circ}{1 - \tan36^\circ \tan9^\circ} = 1\]
\[ \Rightarrow \tan36^\circ + \tan9^\circ = 1 - \tan36^\circ \tan9^\circ\]
\[ \Rightarrow \tan36^\circ + \tan9^\circ + \tan36^\circ \tan9^\circ = 1\]
Hence proved.
APPEARS IN
संबंधित प्रश्न
Prove that `cot^2 pi/6 + cosec (5pi)/6 + 3 tan^2 pi/6 = 6`
Prove the following:
`(cos (pi + x) cos (-x))/(sin(pi - x) cos (pi/2 + x)) = cot^2 x`
Prove the following:
cos2 2x – cos2 6x = sin 4x sin 8x
Prove the following:
`(sin x + sin 3x)/(cos x + cos 3x) = tan 2x`
Prove that: `(cos x - cosy)^2 + (sin x - sin y)^2 = 4 sin^2 (x - y)/2`
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:
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:
cos (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 \[\cos A = - \frac{24}{25}\text{ and }\cos B = \frac{3}{5}\], where π < A < \[\frac{3\pi}{2}\text{ and }\frac{3\pi}{2}\]< B < 2π, find the following:
sin (A + B)
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)
Prove that:
Prove that:
Prove that:
\[\frac{\tan \left( A + B \right)}{\cot \left( A - B \right)} = \frac{\tan^2 A - \tan^2 B}{1 - \tan^2 A \tan^2 B}\]
If tan A + tan B = a and cot A + cot B = b, prove that cot (A + B) \[\frac{1}{a} - \frac{1}{b}\].
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
Prove that:
\[\frac{1}{\sin \left( x - a \right) \sin \left( x - b \right)} = \frac{\cot \left( x - a \right) - \cot \left( x - b \right)}{\sin \left( a - b \right)}\]
If sin α sin β − cos α cos β + 1 = 0, prove that 1 + cot α tan β = 0.
If α + β − γ = π and sin2 α +sin2 β − sin2 γ = λ sin α sin β cos γ, then write the value of λ.
Write the interval in which the value of 5 cos x + 3 cos \[\left( x + \frac{\pi}{3} \right) + 3\] lies.
If tan (A + B) = p and tan (A − B) = q, then write the value of tan 2B.
If sin α − sin β = a and cos α + cos β = b, then write the value of cos (α + β).
If in ∆ABC, tan A + tan B + tan C = 6, then cot A cot B cot C =
The value of \[\cos^2 \left( \frac{\pi}{6} + x \right) - \sin^2 \left( \frac{\pi}{6} - x \right)\] is
If tan (A − B) = 1 and sec (A + B) = \[\frac{2}{\sqrt{3}}\], the smallest positive value of B is
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
Show that 2 sin2β + 4 cos (α + β) sin α sin β + cos 2(α + β) = cos 2α
If tanθ = `(sinalpha - cosalpha)/(sinalpha + cosalpha)`, then show that sinα + cosα = `sqrt(2)` cosθ.
[Hint: Express tanθ = `tan (alpha - pi/4) theta = alpha - pi/4`]
If tanα = `m/(m + 1)`, tanβ = `1/(2m + 1)`, then α + β is equal to ______.
If α + β = `pi/4`, then the value of (1 + tan α)(1 + tan β) is ______.
3(sinx – cosx)4 + 6(sinx + cosx)2 + 4(sin6x + cos6x) = ______.
