Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
Advertisements
उत्तर
`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
LHS = `sinθ(1 + tanθ) + cosθ(1 + cotθ)`
= `sinθ (1 + sinθ/cosθ) + cosθ (1 + cosθ /sinθ)`
= `sinθ((cosθ + sinθ)/cosθ) + cosθ((sinθ + cosθ)/sinθ)`
= `cosθ + sinθ(sinθ /cosθ + cosθ /sinθ)`
= `cosθ + sinθ (1/sinθ 1/cosθ) = secθ + cosecθ `
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
Write the value of cos1° cos 2°........cos180° .
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Find A if tan 2A = cot (A-24°).
Prove that sin4θ - cos4θ = sin2θ - cos2θ
= 2sin2θ - 1
= 1 - 2 cos2θ
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
