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
If tanθ + sinθ = m and tanθ – sinθ = n, show that `m^2 – n^2 = 4\sqrt{mn}.`
If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
If sec θ = `25/7`, then find the value of tan θ.
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ
If cos A = `(2sqrt("m"))/("m" + 1)`, then prove that cosec A = `("m" + 1)/("m" - 1)`
If 2sin2θ – cos2θ = 2, then find the value of θ.
