Advertisements
Advertisements
प्रश्न
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
Advertisements
उत्तर
∠A = 90°, cos B = `"AB"/"BC"`, cos C = `"AC"/"BC"`
∴ L.H.S = cos2 B + cos2 C
= `"Ab"^2/"BC"^2 + "AC"^2/"BC"^2`
= `("AB"^2 + "AC"^2)/"BC"^2`
= `"BC"^2/"BC"^2`
= 1
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the values of `tan ((19pi)/3)`
Find the values of `sin (-(11pi)/3)`
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
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)
Find a quadratic equation whose roots are sin 15° and cos 15°
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
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)`
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Express the following as a sum or difference
sin 35° cos 28°
Show that `cos pi/15 cos (2pi)/15 cos (3pi)/15 cos (4pi)/15 cos (5pi)/15 cos (6pi)/15 cos (7pi)/15 = 1/128`
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
