Advertisements
Advertisements
प्रश्न
Write the value of cosec2 (90° − θ) − tan2 θ.
Advertisements
उत्तर
We have,
`cosec^2 (90°-θ)- tan ^2θ= {cosec(90°-θ)}^2-tan ^2θ`
= `(secθ )^2-tan^2 θ`
= `sec^2 θ-tan ^2 θ`
We know that, ` sec^2 θ-tan ^2θ=1`
Therefore, \[{cosec}^2 \left( 90° - \theta \right) - \tan^2 \theta = 1\]
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
`cot^2 theta - 1/(sin^2 theta ) = -1`a
Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
If x = acosθ , y = bcotθ , prove that `a^2/x^2 - b^2/y^2 = 1.`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`cos 63^circ sec(90^circ - θ) = 1`
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
Prove the following:
`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.
