Advertisements
Advertisements
प्रश्न
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
Advertisements
उत्तर
L.H.S. = cos A (1 + cot A) + sin A (1 + tan A)
= `cosA(1 + cosA/sinA) + sinA(1 + sinA/cosA)`
= `(cosA(sinA + cosA))/sinA + (sinA(cosA + sinA))/cosA`
= `(sinA + cosA)[cosA/sinA + sinA/cosA]`
= `(sinA + cosA)[(cos^2A + sin^2A)/(sinAcosA)]`
= `(sinA + cosA) xx 1/(sinAcosA)`
= `(sinA + cosA)/(sinAcosA)` ...[∵ cos2θ + sin2θ = 1]
= `sinA/(sinAcosA) + cosA/(sinAcosA)`
= `1/cosA + 1/sinA`
= sec A + cosec A = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(1+ secA)/sec A = (sin^2A)/(1-cosA)`
[Hint : Simplify LHS and RHS separately.]
if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2 = 2`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Prove the following identities:
`1 - sin^2A/(1 + cosA) = cosA`
If `sec theta + tan theta = p,` prove that
(i)`sec theta = 1/2 ( p+1/p) (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`
If tanθ `= 3/4` then find the value of secθ.
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
Write 'True' or 'False' and justify your answer in the following:
\[\cos \theta = \frac{a^2 + b^2}{2ab}\], where a and b are two distinct numbers such that ab > 0.
Prove that (1 – cos2A) . sec2B + tan2B (1 – sin2A) = sin2A + tan2B.
(1 – cos2 A) is equal to ______.
