Advertisements
Advertisements
Question
Prove the following identity :
`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`
Advertisements
Solution
LHS = `cosA/(1 - tanA) + sin^2A/(sinA - cosA)`
= `cosA/(1 - sinA/cosA) + sin^2A/(sinA - cosA)`
= `cosA/((cosA - sinA)/(cosA)) + sin^2A/(sinA - cosA)`
= `cos^2A/((cosA - sinA)) - sin^2A/((cosA - sinA))`
= `(cos^2A - sin^2A)/(cosA - sinA) = ((cosA + sinA)(cosA - sinA))/((cosA - sinA))`
= (cosA + sinA)
APPEARS IN
RELATED QUESTIONS
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Without using trigonometric table , evaluate :
`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Prove that : `(sin(90° - θ) tan(90° - θ) sec (90° - θ))/(cosec θ. cos θ. cot θ) = 1`
(1 – cos2 A) is equal to ______.
