Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
उत्तर
In the given question, we need to prove `(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
Using the identity `a^2 - b^2 = (a + b)(a - b)`
`cos theta/((cosec theta + 1)) + cos theta/(cosec theta - 1) = (cos theta(cosec theta - 1)+ cos theta(cosec theta + 1))/(cosec^2 theta - 1)`
`= (cos theta (cosec theta - 1 + cosec theta + 1))/(cosec^2 theta -1) = (cos theta(2 cosec theta))/cot^2 theta`
`= ((2 cos theta)(1/sin theta))/((cos^2 theta/sin^2 theta))`
`= 2 ((cos theta)/(sin theta))(sin^2 theta/cos^2 theta)`
`= 2 sin theta/cos theta`
`= 2 tan theta`
Hence proved.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
If sin θ + cos θ = x, prove that `sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
If tanθ `= 3/4` then find the value of secθ.
Without using trigonometric table , evaluate :
`cosec49°cos41° + (tan31°)/(cot59°)`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`cos 63^circ sec(90^circ - θ) = 1`
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Prove that cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1.
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
If x = a tan θ and y = b sec θ then
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 sec2θ − cos2θ = tan2θ + sin2θ
If tan α + cot α = 2, then tan20α + cot20α = ______.
