Advertisements
Advertisements
प्रश्न
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin2 B + sin2 C = 1
Advertisements
उत्तर
From diagram,
sin B = `"AC"/"BC"`, sin C = `"AB"/"BC"
L.H.S = sin2 B + sin2 C
= `"AC"^2/"BC"^2 + "AB"^2/"BC"^2`
= `("AC"^2 + "AB"^2)/"BC"^2`
= `"BC"^2/"BC"^2`
= 1
= R.H.S
APPEARS IN
संबंधित प्रश्न
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 x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2` find the value of sin(x + y)
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)
Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Find the value of cos 105°.
Prove that cos(π + θ) = − cos θ
Find a quadratic equation whose roots are sin 15° and cos 15°
Prove that cos 8θ cos 2θ = cos25θ – sin23θ
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
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 sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
