Advertisements
Advertisements
प्रश्न
Write the value of the expression \[\frac{1 - 4 \sin 10^\circ \sin 70^\circ}{2 \sin 10^\circ}\]
उत्तर
\[\frac{1 - 4\sin10^\circ \sin70^\circ}{2\sin10^\circ}\]
\[ = \frac{1 - 2\left[ 2\sin10^\circ \sin70^\circ \right]}{2\sin10^\circ}\]
\[ = \frac{1 - 2\left[ \cos\left( 10^\circ - 70^\circ \right) - \cos\left( 10^\circ + 70^\circ \right) \right]}{2\sin10^\circ}\]
\[ = \frac{1 - 2\left[ \cos\left( - 60^\circ \right) - \cos80^\circ \right]}{2\sin10^\circ}\]
\[ = \frac{1 - 2\left[ \cos60^\circ - \cos80^\circ \right]}{2\sin10^\circ}\]
\[ = \frac{1 - 2\left[ \frac{1}{2} - \cos\left( 90^\circ - 10^\circ \right) \right]}{2\sin10^\circ}\]
\[ = \frac{1 - 2 \times \frac{1}{2} + 2\cos\left( 90^\circ - 10^\circ \right)}{2\sin10^\circ}\]
\[ = \frac{2\sin10^\circ}{2\sin10^\circ}\]
\[ = 1\]
APPEARS IN
संबंधित प्रश्न
Prove that:
sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]
Prove that:
tan 20° tan 40° tan 60° tan 80° = 3
Prove that tan 20° tan 30° tan 40° tan 80° = 1.
Show that:
sin A sin (B − C) + sin B sin (C − A) + sin C sin (A − B) = 0
Express each of the following as the product of sines and cosines:
sin 5x − sin x
Prove that:
sin 50° + sin 10° = cos 20°
Prove that:
sin 50° − sin 70° + sin 10° = 0
Prove that:
cos 20° + cos 100° + cos 140° = 0
Prove that:
Prove that:
Prove that:
Prove that:
cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A cos 6A
Prove that:
cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A
Prove that:
`sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
If \[m \sin\theta = n \sin\left( \theta + 2\alpha \right)\], prove that \[\tan\left( \theta + \alpha \right) \cot\alpha = \frac{m + n}{m - n}\]
If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].
If A + B = \[\frac{\pi}{3}\] and cos A + cos B = 1, then find the value of cos \[\frac{A - B}{2}\].
Write the value of \[\sin\frac{\pi}{15}\sin\frac{4\pi}{15}\sin\frac{3\pi}{10}\]
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
If sin α + sin β = a and cos α − cos β = b, then tan \[\frac{\alpha - \beta}{2}\]=
cos 35° + cos 85° + cos 155° =
The value of sin 50° − sin 70° + sin 10° is equal to
If sin (B + C − A), sin (C + A − B), sin (A + B − C) are in A.P., then cot A, cot B and cot Care in
If sin x + sin y = \[\sqrt{3}\] (cos y − cos x), then sin 3x + sin 3y =
If \[\tan\alpha = \frac{x}{x + 1}\] and
Express the following as the sum or difference of sine or cosine:
`cos (7"A")/3 sin (5"A")/3`
Prove that:
cos 20° cos 40° cos 80° = `1/8`
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
Evaluate-
cos 20° + cos 100° + cos 140°
If cosec A + sec A = cosec B + sec B prove that cot`(("A + B"))/2` = tan A tan B.
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
If secx cos5x + 1 = 0, where 0 < x ≤ `pi/2`, then find the value of x.
