Advertisements
Advertisements
प्रश्न
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 2
Advertisements
उत्तर
LHS = sin2 10° + sin2 20° + sin2 70° + sin2 80°
= sin2 10° + sin2 (90° – 10°) + sin2 20° + sin2(90° – 20°)
= sin2 10° + (cos 10°)2 + sin2 20° + (cos 20°)2
= (sin2 10+ cos2 10) + sin2 20° + cos2 20°
= 1 + 1
= 2
= R.H.S
APPEARS IN
संबंधित प्रश्न
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Show that tan 75° + cot 75° = 4
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Express the following as a product
sin 50° + sin 40°
Show that sin 12° sin 48° sin 54° = `1/8`
Prove that `sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2` = sin 2θ sin 5θ
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
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 ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos2 B + cos2 C = 1
