Advertisements
Advertisements
प्रश्न
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
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
Prove that cos(π + θ) = − cos θ
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
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 `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Express the following as a sum or difference
sin 35° cos 28°
Express the following as a sum or difference
sin 4x cos 2x
Express the following as a sum or difference
2 sin 10θ cos 2θ
Express the following as a product
cos 35° – cos 75°
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Prove that `(sin 4x + sin 2x)/(cos 4x + cos 2x)` = tan 3x
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
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 sin2 B + sin2 C = 1
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
