Advertisements
Advertisements
Question
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
Advertisements
Solution
2 `(x^2 - 1/(x^2))`
=`4/2(x^2 - 1/(x^2))`
=`1/2(4x^2 - 4/(x^2))`
=`1/2 [(2x)^2- (2/x)^2]`
=`1/2 [( cosec theta )^2 - (cot theta)^2]`
=`1/2 (cosec ^2 theta - cot^2 theta)`
=`1/2 (1)`
=`1/2`
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
sec2A + cosec2A = sec2A . cosec2A
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
If `secθ = 25/7 ` then find tanθ.
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
Prove that:
tan (55° + x) = cot (35° – x)
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Prove that cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1.
Prove that `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2 = 1`
Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.
Activity:
L.H.S = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` .....`[sin^2"A" + square = 1]`
= `square` – cos2A .....[sin2A = 1 – cos2A]
= `square`
= R.H.S
If tan θ = `7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ......[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square` .......`[cos theta = 1/sectheta]`
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
