Advertisements
Advertisements
प्रश्न
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
Advertisements
उत्तर
`(1+ tan^2 theta )(1+ sin theta )(1- sintheta)`
=` sec^2 theta (1- sin^2 theta )`
=`1/ cos^2 theta xx cos^2 theta`
= 1
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Prove the following trigonometric identities
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove that
`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
`cos^2 theta + 1/((1+ cot^2 theta )) =1`
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
If `( sin theta + cos theta ) = sqrt(2) , " prove that " cot theta = ( sqrt(2)+1)`.
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
Prove the following identity :
`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
tan θ cosec2 θ – tan θ is equal to
If cos θ = `24/25`, then sin θ = ?
If 3 sin θ = 4 cos θ, then sec θ = ?
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`
Prove the following trigonometry identity:
(sin θ + cos θ)(cosec θ – sec θ) = cosec θ ⋅ sec θ – 2 tan θ
