Advertisements
Advertisements
प्रश्न
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
Advertisements
उत्तर
L.H.S. = (m2 + n2) cos2 B
= `(cos^2A/cos^2B + cos^2A/sin^2B)cos^2B`
= `((cos^2Asin^2B + cos^2Acos^2B)/(cos^2Bsin^2B))cos^2B`
= `((cos^2Asin^2B + cos^2Acos^2B)/sin^2B)`
= `(cos^2A(sin^2B + cos^2B))/sin^2B`
= `cos^2A/sin^2B`
= n2
Hence, (m2 + n2) cos2 B = n2.
संबंधित प्रश्न
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Prove the following identity :
`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Prove that:
tan (55° + x) = cot (35° – x)
