Advertisements
Advertisements
प्रश्न
Prove that:
Advertisements
उत्तर
Consider LHS:
\[\cos \left( \frac{\pi}{4} + x \right) + \cos\left( \frac{\pi}{4} - x \right)\]
\[ = 2\cos \left\{ \frac{\left( \frac{\pi}{4} + x \right) + \left( \frac{\pi}{4} - x \right)}{2} \right\}\cos \left\{ \frac{\left( \frac{\pi}{4} + x \right) - \left( \frac{\pi}{4} + x \right)}{2} \right\} \left\{ \because \cos A + \cos B = 2\cos \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right) \right\}\]
\[= 2\cos \left\{ \frac{\frac{\pi}{4} + x + \frac{\pi}{4} - x}{2} \right\}\cos \left\{ \frac{\frac{\pi}{4} + x - \frac{\pi}{4} + x}{2} \right\}\]
\[ = 2\cos$\left( \frac{\pi}{4} \right)$ \cos x\]
\[ = 2 \times \frac{1}{\sqrt{2}} \times \cos x\]
\[ = \sqrt{2}\cos x\]
= RHS
Hence, LHS = RHS
APPEARS IN
संबंधित प्रश्न
Prove that:
Show that :
Show that :
Prove that:
tan 20° tan 40° tan 60° tan 80° = 3
Prove that:
sin 20° sin 40° sin 60° sin 80° = \[\frac{3}{16}\]
Express each of the following as the product of sines and cosines:
cos 12x - cos 4x
Express each of the following as the product of sines and cosines:
sin 2x + cos 4x
Prove that:
sin 40° + sin 20° = cos 10°
Prove that:
cos 80° + cos 40° − cos 20° = 0
Prove that:
\[\sin\frac{5\pi}{18} - \cos\frac{4\pi}{9} = \sqrt{3} \sin\frac{\pi}{9}\]
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
Write the value of sin \[\frac{\pi}{12}\] sin \[\frac{5\pi}{12}\].
If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].
The value of sin 78° − sin 66° − sin 42° + sin 60° is ______.
cos 35° + cos 85° + cos 155° =
If cos A = m cos B, then \[\cot\frac{A + B}{2} \cot\frac{B - A}{2}\]=
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 =
Express the following as the sum or difference of sine or cosine:
`sin "A"/8 sin (3"A")/8`
Express the following as the sum or difference of sine or cosine:
`cos (7"A")/3 sin (5"A")/3`
Express the following as the product of sine and cosine.
sin A + sin 2A
Express the following as the product of sine and cosine.
cos 2A + cos 4A
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
Prove that:
sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
Evaluate-
cos 20° + cos 100° + cos 140°
If sin(y + z – x), sin(z + x – y), sin(x + y – z) are in A.P, then prove that tan x, tan y and tan z are in A.P.
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:
