Advertisements
Advertisements
प्रश्न
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3
Advertisements
उत्तर
3 sin A + 5 cos A = 5 ....[Given]
∴ (3 sin A + 5 cos A)2 = 25 ......[Squaring both the sides]
∴ 9 sin2A + 30 sin A cos A + 25 cos2A = 25
∴ 9(1 – cos2A) + 30 sin A cos A + 25(1 – sin2A) = 25
∴ 9 – 9 cos2A + 30 sin A cos A + 25 – 25 sin2A = 25
∴ 25 sin2A – 30 sin A cos A + 9 cos2A = 9
∴ (5 sin A – 3 cos A)2 = 9 ......[∵ a2 – 2ab + b2 = (a – b)2]
∴ 5 sin A – 3 cos A = ± 3 .....[Taking square root of both sides]
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) 2 (sin^6 θ + cos^6 θ) –3(sin^4 θ + cos^4 θ) + 1 = 0`
`(ii) (sin^8 θ – cos^8 θ) = (sin^2 θ – cos^2 θ) (1 – 2sin^2 θ cos^2 θ)`
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
Prove the following trigonometric identities.
`tan^2 theta - sin^2 theta tan^2 theta sin^2 theta`
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
9 sec2 A − 9 tan2 A is equal to
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove that:
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
Without using trigonometric identity , show that :
`sin(50^circ + θ) - cos(40^circ - θ) = 0`
Prove that `(cos θ)/(1 - sin θ) = (1 + sin θ)/(cos θ)`.
Prove that `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2 = 1`
Prove that `(sin^2theta)/(cos theta) + cos theta` = sec θ
If cosec A – sin A = p and sec A – cos A = q, then prove that `("p"^2"q")^(2/3) + ("pq"^2)^(2/3)` = 1
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
