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
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Find the value of cos 105°.
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
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 cos 2A, A lies in the first quadrant, when cos A = `15/17`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
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 sum or difference
sin 4x cos 2x
Show that sin 12° sin 48° sin 54° = `1/8`
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
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`
