Advertisements
Advertisements
प्रश्न
If secx cos5x + 1 = 0, where 0 < x ≤ `pi/2`, then find the value of x.
Advertisements
उत्तर
secx cos5x = –1
⇒ cos5x = `(-1)/secx`
We know that
secx = `1/cosx`
⇒ cos5x + cosx = 0
By transformation formula of T-ratios,
We know that
cosA + cosB = `2cos(("A" + "B")/2) cos(("A" - "B")/2)`
⇒ `2cos((5x + x)/2) cos((5x - x)/2)` = 0
⇒ 2cos3x cos2x = 0
⇒ cos3x = 0 or cos2x = 0
∵ 0 < x ≤ `pi/2`
Therefore, 0 < 2x ≤ π or 0 < 3x ≤ `(3pi)/2`
Therefore, 2x = `pi/2`
⇒ x = `pi/4`
3x = `pi/2`
⇒ x = `pi/6`
Or 3x = `(3pi)/2`
⇒ x = `pi/2`
Hence, x = `pi/6, pi/4, pi/2`.
APPEARS IN
संबंधित प्रश्न
Prove that:
Show that :
Prove that:
cos 10° cos 30° cos 50° cos 70° = \[\frac{3}{16}\]
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
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 \[\frac{1}{2}\].
Express each of the following as the product of sines and cosines:
sin 2x + cos 4x
Prove that:
cos 100° + cos 20° = cos 40°
Prove that:
sin 40° + sin 20° = cos 10°
Prove that:
\[\sin\frac{5\pi}{18} - \cos\frac{4\pi}{9} = \sqrt{3} \sin\frac{\pi}{9}\]
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:
Prove that:
Prove that:
Prove that:
Prove that:
cos (A + B + C) + cos (A − B + C) + cos (A + B − C) + cos (− A + B + C) = 4 cos A cos Bcos C
If y sin ϕ = x sin (2θ + ϕ), prove that (x + y) cot (θ + ϕ) = (y − x) cot θ.
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
If sin 2 θ + sin 2 ϕ = \[\frac{1}{2}\] and cos 2 θ + cos 2 ϕ = \[\frac{3}{2}\], then cos2 (θ − ϕ) =
The value of cos 52° + cos 68° + cos 172° is
Express the following as the sum or difference of sine or cosine:
cos(60° + A) sin(120° + A)
Express the following as the sum or difference of sine or cosine:
cos 7θ sin 3θ
Express the following as the product of sine and cosine.
sin A + sin 2A
Prove that:
sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A
Evaluate:
sin 50° – sin 70° + sin 10°
If tan θ = `1/sqrt5` and θ lies in the first quadrant then cos θ is:
