Advertisements
Advertisements
Question
If P, Q and R are the interior angles of ΔPQR, prove that `cot(("Q" + "R")/2) = tan "P"/(2)`
Advertisements
Solution
Since P, Q and R are interior angles of ΔPQR,
P + Q + R = 180°
⇒ Q + R = 180° - P
Now,
L.H.S. = `cot (("Q" + "R")/2)`
= `cot ((180° - "P")/2)`
= `cot(90° - "P"/2)`
= `tan "P"/(2)`
= R.H.S.
APPEARS IN
RELATED QUESTIONS
Calculate the value of A, if (sin A - 1) (2 cos A - 1) = 0
Solve the following equation for A, if sec 2A = 2
Find the value of 'A', if cot 3A = 1
Evaluate the following: `((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)` if θ = 30°
Find the value 'x', if:
Find the value 'x', if:
If tan x° = `(5)/(12) . tan y° = (3)/(4)` and AB = 48m; find the length CD.
Evaluate the following: `(sin62°)/(cos28°)`
Express each of the following in terms of trigonometric ratios of angles between 0° and 45°: tan77° - cot63° + sin57°
Evaluate the following: tan(78° + θ) + cosec(42° + θ) - cot(12° - θ) - sec(48° - θ)
