Advertisements
Advertisements
प्रश्न
If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.
Advertisements
उत्तर
Given 3 sin θ + 5 cos θ = 5
Squaring on both sides for both the equations
⇒ 9 sin2θ + 25 cos2θ + 30 sinθ cosθ = 25
⇒ 25 sin2θ + 9 cos2θ − 30 sinθ cosθ = x2
Adding the equations;
⇒ 34 (sin2θ + cos2θ) = 25 + x2
⇒ x2 = 34 − 25 = 9
⇒ x = ±3
∴ 5 sinθ − 3 cosθ = ±3
Hence proved.
APPEARS IN
संबंधित प्रश्न
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, then prove that x2 + y2 = 1
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
