Advertisements
Advertisements
Question
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Advertisements
Solution
sinθcotθ + sinθcosecθ = 1 + cosθ
LHS = `sinθcosθ/sinθ + sinθ1/sinθ`
= cosθ + 1 = RHS
APPEARS IN
RELATED QUESTIONS
`(1-cos^2theta) sec^2 theta = tan^2 theta`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
Show that none of the following is an identity:
`tan^2 theta + sin theta = cos^2 theta`
If `secθ = 25/7 ` then find tanθ.
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 that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
If x = h + a cos θ, y = k + b sin θ.
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.
Prove that `(sin θ)/(sec θ + 1) + (sin θ)/(sec θ - 1) = 2 cot θ`.
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
