Advertisements
Advertisements
Question
If secx cos5x + 1 = 0, where 0 < x ≤ `pi/2`, then find the value of x.
Advertisements
Solution
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
RELATED QUESTIONS
Prove that:
Show that :
Prove that:
cos 40° cos 80° cos 160° = \[- \frac{1}{8}\]
Prove that:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]
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
Prove that:
cos 80° + cos 40° − cos 20° = 0
Prove that:
cos 20° + cos 100° + cos 140° = 0
Prove that:
Prove that:
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:
cos (A + B + C) + cos (A − B + C) + cos (A + B − C) + cos (− A + B + C) = 4 cos A cos Bcos C
If cosec A + sec A = cosec B + sec B, prove that tan A tan B = \[\cot\frac{A + B}{2}\].
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 \[\sin\frac{\pi}{15}\sin\frac{4\pi}{15}\sin\frac{3\pi}{10}\]
sin 163° cos 347° + sin 73° sin 167° =
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 product of sine and cosine.
cos 2A + cos 4A
Express the following as the product of sine and cosine.
sin 6θ – sin 2θ
Express the following as the product of sine and cosine.
cos 2θ – cos θ
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
Prove that:
sin (A – B) sin C + sin (B – C) sin A + sin(C – A) sin B = 0
Prove that:
2 cos `pi/13` cos \[\frac{9\pi}{13} + \text{cos} \frac{3\pi}{13} + \text{cos} \frac{5\pi}{13}\] = 0
Prove that cos 20° cos 40° cos 60° cos 80° = `3/16`.
Evaluate:
sin 50° – sin 70° + sin 10°
If cos A + cos B = `1/2` and sin A + sin B = `1/4`, prove that tan `(("A + B")/2) = 1/2`
