Advertisements
Advertisements
प्रश्न
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Advertisements
उत्तर
`(m^2 - 1)/(m^2 + 1)`
⇒ `((sectheta + tantheta)^2 - (sec^2theta - tan^2theta))/((sectheta + tantheta)^2 + (sec^2theta - tan^2theta))`
⇒ `(sec^2theta + tan^2theta + 2sectheta tantheta - sec^2theta + tan^2theta)/(sec^2theta + tan^2theta + 2sectheta tantheta + sec^2theta - tan^2theta)`
⇒ `(2tantheta(tantheta + sectheta))/(2sectheta(tantheta + sectheta))`
⇒ `tantheta/sectheta = sintheta/(costheta sectheta)` `(∵ tantheta = sintheta/costheta)`
⇒ `sintheta/(costheta xx 1/costheta) = sin theta` `(∵ costheta = 1/sectheta)`
Hence, proved
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
`cot^2 theta - 1/(sin^2 theta ) = -1`a
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Write the value of cosec2 (90° − θ) − tan2 θ.
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
