Advertisements
Advertisements
Question
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Solution
L.H.S. = (sec A – cos A) (sec A + cos A)
= sec2 A – cos2 A
= (1 + tan2 A) – (1 – sin2 A)
= sin2 A + tan2 A
= R.H.S.
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
Prove that
`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`
` tan^2 theta - 1/( cos^2 theta )=-1`
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
If 2sin2θ – cos2θ = 2, then find the value of θ.
