Advertisements
Advertisements
प्रश्न
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
Advertisements
उत्तर
cot(A + B) = `1/(tan("A" + "B"))`
= `1/((tan "A" + tan "B")/(1 - tan "A" tan "B"))`
= `(1 - tan"A" tan"B")/(tan"A" + tan "B")`
= `(1 - 1/cot"A" * 1/cot"B")/(1/cot "A" + 1/cot"B")`
= `((cot"A" cot"B" - 1)/(cot"A" cot"B"))/((cot"B" + cot"A")/(cot"A" cot"B"))`
cot(A + B) = `(cot"A" cot"B" - 1)/(cot"A" + cot"B")`
APPEARS IN
संबंधित प्रश्न
Find the values of cos(300°)
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
If sin A = `3/5` and cos B = `9/41, 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of cos(A – B)
Prove that cos(π + θ) = − cos θ
Prove that sin(45° + θ) – sin(45° – θ) = `sqrt(2) sin θ`
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Express the following as a product
cos 35° – cos 75°
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
