Advertisements
Advertisements
प्रश्न
If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x2 + y2 = m2 + n2
Advertisements
उत्तर
m2 + n2
= (x cos A + y sin A)2 + (x sin A – y cos A)2
= x2 cos2 A + y2 sin2 A + 2xy sin A cos A + x2 sin2 A + y2 cos2 A – 2xy sin A cos A
= x2 (cos2 A + sin2 A) + y2 (cos2 A + sin2 A)
= x2 + y2
Hence, x2 + y2 = m2 + n2
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.]
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Choose the correct alternative:
1 + tan2 θ = ?
Prove the following:
`1 + (cot^2 alpha)/(1 + "cosec" alpha)` = cosec α
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
Eliminate θ if x = r cosθ and y = r sinθ.
