Advertisements
Advertisements
प्रश्न
(secA + tanA) (1 − sinA) = ______.
विकल्प
sec A
sin A
cosec A
cos A
Advertisements
उत्तर
(secA + tanA) (1 − sinA) = cos A.
Explanation:
(secA + tanA) (1 − sinA)
= `(1/cosA+sinA/cosA)(1-sinA)`
= `((1+sinA)/cosA)(1-sinA)`
= `(1-sin^2A)/(cosA)`
= `(cos^2A)/cos A`
= cosA
Hence, alternative cosA is correct.
APPEARS IN
संबंधित प्रश्न
Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec2 θ = 1 + tan2 θ.
9 sec2 A − 9 tan2 A = ______.
Prove the following trigonometric identities.
`sin theta/(1 - cos theta) = cosec theta + cot theta`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Prove the following trigonometric identities.
`(1 + cos θ + sin θ)/(1 + cos θ - sin θ) = (1 + sin θ)/cos θ`
Prove the following identities:
`1/(secA + tanA) = secA - tanA`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
(i)` (1-cos^2 theta )cosec^2theta = 1`
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
Prove the following identity :
`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Choose the correct alternative:
tan (90 – θ) = ?
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
