Advertisements
Advertisements
प्रश्न
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Advertisements
उत्तर
LHS = secA(1 + sinA)(secA - tanA)
= `1/cosA(1 + sinA)(1/cosA - sinA/cosA)`
= `((1 + sinA))/cosA((1-sinA)/cosA) = (1-sin^2A)/cos^2A`
= `(cos^2A/cos^2A) = 1` = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`( i)sin^{2}A/cos^{2}A+\cos^{2}A/sin^{2}A=\frac{1}{sin^{2}Acos^{2}A)-2`
`(ii)\frac{cosA}{1tanA}+\sin^{2}A/(sinAcosA)=\sin A\text{}+\cos A`
`( iii)((1+sin\theta )^{2}+(1sin\theta)^{2})/cos^{2}\theta =2( \frac{1+sin^{2}\theta}{1-sin^{2}\theta } )`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Find the value of sin 30° + cos 60°.
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
Prove that `(sin θ)/(sec θ + 1) + (sin θ)/(sec θ - 1) = 2 cot θ`.
If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.
If 2sin2θ – cos2θ = 2, then find the value of θ.
