Advertisements
Advertisements
प्रश्न
\[\frac{x^2 - 1}{2x}\] is equal to
विकल्प
sec θ + tan θ
sec θ − tan θ
sec2 θ + tan2 θ
sec2 θ − tan2 θ
Advertisements
उत्तर
The given expression is `sqrt ((1+sinθ)/(1-sinθ))`
Multiplying both the numerator and denominator under the root by `1+ sinθ`, we have
`sqrt (((1+ sinθ)(1+sin θ))/((1+sin θ)(1-sinθ)))`
`=sqrt((1+sinθ)/((1- sin^2θ)))`
`= sqrt((1+ sinθ)^2/cos^2θ)`
=`(1+sinθ)/cosθ`
=` 1/cosθ+sinθ/cosθ`
=` sec θ+tan θ`
APPEARS IN
संबंधित प्रश्न
Prove that `cosA/(1+sinA) + tan A = secA`
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
`(cos ec^theta + cot theta )/( cos ec theta - cot theta ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta cot theta`
If `(x/a sin a - y/b cos theta) = 1 and (x/a cos theta + y/b sin theta ) =1, " prove that "(x^2/a^2 + y^2/b^2 ) =2`
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove that sin θ (1 – tan θ) – cos θ (1 – cot θ) = cosec θ – sec θ
Prove the following:
`1 + (cot^2 alpha)/(1 + "cosec" alpha)` = cosec α
