Advertisements
Advertisements
प्रश्न
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
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
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following trigonometric identities.
sin2 A cot2 A + cos2 A tan2 A = 1
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
`sqrt((1+sin theta)/(1-sin theta)) = (sec theta + tan theta)`
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
Define an identity.
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Prove that sec2 (90° - θ) + tan2 (90° - θ) = 1 + 2 cot2 θ.
If tan θ × A = sin θ, then A = ?
Prove that `sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
