Advertisements
Advertisements
प्रश्न
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Advertisements
उत्तर
(1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
= `(1 + sinθ/cosθ + 1/cosθ)(1 + cosθ/sinθ - 1/sinθ)`
= `((cosθ + sinθ + 1)/cosθ)((sinθ + cosθ - 1)/sinθ)`
= `((sinθ + cosθ)^2 - (1)^2)/(sinθcosθ)`
= `(sin^2θ + cos^2θ + 2sinθ cosθ - 1)/(sinθcosθ)`
= `(1 + 2sinθ cosθ - 1)/(sinθcosθ)`
= `(2sinθ cosθ)/(sinθ cosθ) = 2`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
sec2A + cosec2A = sec2A . cosec2A
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
Prove that sin4θ - cos4θ = sin2θ - cos2θ
= 2sin2θ - 1
= 1 - 2 cos2θ
Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
If tan θ = `7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ......[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square` .......`[cos theta = 1/sectheta]`
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
