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
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove the following trigonometric identities
`((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) = (1 + sin^2 theta)/(1 - sin^2 theta)`
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
Prove that:
`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.
If \[\sin \theta = \frac{1}{3}\] then find the value of 9tan2 θ + 9.
If \[sec\theta + tan\theta = x\] then \[tan\theta =\]
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Without using trigonometric identity , show that :
`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.
