Advertisements
Advertisements
Question
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
Advertisements
Solution
LHS = `cos theta/((1-tan theta))-sin^2theta/((cos theta-sintheta))`
=`cos theta/((1-sintheta/costheta)) -sin^2 theta/((cos theta-sin theta))`
=`cos^2 theta/((cos theta-sintheta))- sin^2 theta/((cos theta-sin theta))`
=`(cos^2 theta- sin ^2 theta)/((cos theta- sin theta))`
=`((costheta + sin theta)( cos theta-sin theta))/((cos theta - sin theta))`
=`(cos theta + sin theta)`
= RHS
Hence, LHS = RHS
APPEARS IN
RELATED QUESTIONS
9 sec2 A − 9 tan2 A = ______.
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove the following trigonometric identity.
`(sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)`
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x2 + y2 + z2 = r2
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Prove the following identity :
`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
sin2θ + sin2(90 – θ) = ?
Which is not correct formula?
If `tan θ = 9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ...[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3.
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
