Advertisements
Advertisements
Question
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
Advertisements
Solution
LHS = `(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")`
`= (2 cos ((7"A" + 5"A")/2) cos((7"A" - 5"A")/2))/(2 cos ((7"A" + 5"A")/2) sin((7"A" - 5"A")/2))`
`[∵ cos "C" + cos "D" = 2 cos (("C + D")/2) cos (("C - D")/2)]`
`= (2 cos 6"A" cos "A")/(2 cos 6"A" sin "A")`
`= (cos "A")/(sin "A")`
= cot A = RHS
Hence proved.
APPEARS IN
RELATED QUESTIONS
Prove that:
Show that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
Prove that:
sin 50° − sin 70° + sin 10° = 0
Prove that:
cos 20° + cos 100° + cos 140° = 0
Prove that:
Prove that:
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.
Express the following as the product of sine and cosine.
sin 6θ – sin 2θ
Prove that:
sin A sin(60° + A) sin(60° – A) = `1/4` sin 3A
Prove that:
2 cos `pi/13` cos \[\frac{9\pi}{13} + \text{cos} \frac{3\pi}{13} + \text{cos} \frac{5\pi}{13}\] = 0
