Advertisements
Advertisements
Question
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
Advertisements
Solution
LHS = `(sin^2θ)/(cosθ) + cosθ = secθ`
= `(sin^2θ + cos^2θ)/(cosθ)`
= `1/(cosθ)` ...(sin2θ + cos2θ = 1)
= secθ ...`(1/cosθ = secθ)`
R.H.S
LHS = RHS
Hence proved.
RELATED QUESTIONS
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove that
`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
cos4 A − sin4 A is equal to ______.
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle.
Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ) + cos2 θ.
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
If cosA + cos2A = 1, then sin2A + sin4A = 1.
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
