Advertisements
Advertisements
प्रश्न
Prove that:
`tanA/(1 - cotA) + cotA/(1 - tanA) = secA "cosec" A + 1`
Advertisements
उत्तर
L.H.S. = `tanA/(1 - cotA) + cotA/(1 - tanA)`
= `tanA/(1 - 1/tanA) + (1/tanA)/(1 - tanA)`
= `tan^2A/(tanA - 1) + 1/(tanA(1 - tanA))`
= `(tan^3A - 1)/(tanA(1 - tanA))`
= `((tanA - 1)(tan^2A + 1 + tanA))/(tanA(tanA - 1)`
= `(sec^2A + tanA)/tanA`
= `(1/cos^2A)/(sinA/cosA) + 1`
= `1/(sinAcosA) + 1`
= sec A cosec A + 1 = R.H.S.
APPEARS IN
संबंधित प्रश्न
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
If `sec theta + tan theta = p,` prove that
(i)`sec theta = 1/2 ( p+1/p) (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
What is the value of 9cot2 θ − 9cosec2 θ?
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
If `tan θ = 9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ...[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
