Advertisements
Advertisements
प्रश्न
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Advertisements
उत्तर
L.H.S. = (1 + cot A – cosec A)(1 + tan A + sec A)
= `(1 + cosA/sinA - 1/sinA)(1 + sinA/cosA + 1/cosA)`
= `((sinA + cosA - 1)/sinA)((cosA + sinA + 1)/cosA)`
= `((sinA + cosA - 1)(sinA + cosA + 1))/(sinAcosA)`
= `((sinA + cosA)^2 - (1)^2)/(sinAcosA)`
= `(sin^2A + cos^2A + 2sinAcosA - 1)/(sinAcosA)`
= `(1 + 2sinAcosA - 1)/(sinAcosA)`
= `(2sinAcosA)/(sinAcosA)`
= 2 = R.H.S.
APPEARS IN
संबंधित प्रश्न
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`
`(1 + cot^2 theta ) sin^2 theta =1`
If tan A = n tan B and sin A = m sin B , prove that `cos^2 A = ((m^2-1))/((n^2 - 1))`
Write the value of `4 tan^2 theta - 4/ cos^2 theta`
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
Prove that cot2θ – tan2θ = cosec2θ – sec2θ.
