Advertisements
Advertisements
Question
Prove that:
`(cos 7"A" +cos 5"A")/(sin 7"A" −sin 5"A")` = cot A
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:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]
Prove that:
Prove that:
Prove that:
Prove that:
Prove that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
Write the value of the expression \[\frac{1 - 4 \sin 10^\circ \sin 70^\circ}{2 \sin 10^\circ}\]
cos 40° + cos 80° + cos 160° + cos 240° =
If A, B, C are in A.P., then \[\frac{\sin A - \sin C}{\cos C - \cos A}\]=
Find the value of tan22°30′. `["Hint:" "Let" θ = 45°, "use" tan theta/2 = (sin theta/2)/(cos theta/2) = (2sin theta/2 cos theta/2)/(2cos^2 theta/2) = sintheta/(1 + costheta)]`
