Advertisements
Advertisements
प्रश्न
Prove that:
Advertisements
उत्तर
Consider LHS:
\[\sin 65^\circ + \cos 65^\circ\]
\[ = \sin 65^\circ + \cos \left( 90^\circ - 25^\circ \right)\]
\[ = \sin 65^\circ + \sin 25^\circ\]
\[ = 2\sin \left( \frac{65^\circ + 25^\circ}{2} \right) \cos \left( \frac{65^\circ - 25^\circ}{2} \right) \left\{ \because \sin A + \sin B = 2\sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right) \right\}\]
\[ = 2\sin 45^\circ \cos 20^\circ\]
\[ = 2 \times \frac{1}{\sqrt{2}} \cos 20^\circ\]
\[ = \sqrt{2}\cos 20^\circ\]
= RHS
Hence, LHS = RHS.
APPEARS IN
संबंधित प्रश्न
Show that :
Show that :
Prove that:
sin 20° sin 40° sin 80° = \[\frac{\sqrt{3}}{8}\]
Show that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
If α + β = \[\frac{\pi}{2}\], show that the maximum value of cos α cos β is \[\frac{1}{2}\].
Prove that:
sin 105° + cos 105° = cos 45°
Prove that:
sin 50° − sin 70° + sin 10° = 0
Prove that:
cos 20° + cos 100° + cos 140° = 0
Prove that:
Prove that:
Prove that:
`sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`
Prove that:
sin 3A + sin 2A − sin A = 4 sin A cos \[\frac{A}{2}\] \[\frac{3A}{2}\]
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
If \[x \cos\theta = y \cos\left( \theta + \frac{2\pi}{3} \right) = z \cos\left( \theta + \frac{4\pi}{3} \right)\], prove that \[xy + yz + zx = 0\]
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 α + cos β)2 + (sin α + sin β)2 = \[\lambda \cos^2 \left( \frac{\alpha - \beta}{2} \right)\], write the value of λ.
Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].
sin 163° cos 347° + sin 73° sin 167° =
If sin α + sin β = a and cos α − cos β = b, then tan \[\frac{\alpha - \beta}{2}\]=
The value of sin 50° − sin 70° + sin 10° is equal to
sin 47° + sin 61° − sin 11° − sin 25° 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
Express the following as the sum or difference of sine or cosine:
cos(60° + A) sin(120° + A)
Express the following as the product of sine and cosine.
sin 6θ – sin 2θ
Prove that:
cos 20° cos 40° cos 80° = `1/8`
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
Evaluate:
sin 50° – sin 70° + sin 10°
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
