Advertisements
Advertisements
Question
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Advertisements
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.
RELATED QUESTIONS
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, then\[\frac{x^2}{a^2} + \frac{y^2}{b^2}\]
Prove the following identity :
`(1 + cotA + tanA)(sinA - cosA) = secA/(cosec^2A) - (cosecA)/sec^2A`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
If sec θ = `25/7`, then find the value of tan θ.
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
