Advertisements
Advertisements
Question
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
Advertisements
Solution
LHS = `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ))`
LHS = `(sin^2 θ/cos θ). (cos^2 θ/sin θ)`
LHS = sin θ. cos θ
RHS = `1/(tan θ + cot θ)`
RHS = `1/((sin^2 θ + cos^2 θ)/(sin θ. cos θ))`
RHS = `(sin θ. cos θ)/(sin^2 θ + cos^2 θ)`
RHS = sin θ. cos θ
LHS = RHS
Hence proved.
RELATED QUESTIONS
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
If tan A = n tan B and sin A = m sin B , prove that `cos^2 A = ((m^2-1))/((n^2 - 1))`
Write the value of cos1° cos 2°........cos180° .
Find the value of `(cos 38° cosec 52°)/(tan 18° tan 35° tan 60° tan 72° tan 55°)`
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
Prove that: `1/(sec θ - tan θ) = sec θ + tan θ`.
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, then prove that x2 + y2 = 1
