Advertisements
Advertisements
Question
If sinA + cosA = m and secA + cosecA = n , prove that n(m2 - 1) = 2m
Advertisements
Solution
Given : sin θ + cos θ = m and secθ + cosecθ = n
Consider L.H.S. = n(m2 - 1) = (secθ + cosecθ)[(sinθ + cosθ)2 - 1]
= `(1/cosθ + 1/sinθ) [sin^2θ + cos^2θ + 2sinθcosθ - 1`]
= `((cosθ + sinθ)/(sinθcosθ)) (1 + 2sinθcosθ - 1)`
= `((cosθ + sinθ))/(sinθcosθ) (2 sinθ cosθ)`
= 2(sinθ + cosθ)
= 2m = R.H.S.
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =
Prove the following identity :
`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`
Prove the following identity :
`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`
