Advertisements
Advertisements
Question
If `sec alpha=2/sqrt3` , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.
Advertisements
Solution
Given that α is in quadrant IV, where x is positive and y is negative.
`sec alpha=r/x=2/sqrt3`
`Let r=2k, `
`r^2=x^2+y^2`
`therefore(2k^2)=(sqrt(3k))^2+y^2`
`therefore y^2=4k^2-3k^2=k^2`
`therefore y=+-k`
`cosec alpha =r/y=(2k)/-k=-2`
Substituting the value of cosec ,we get
`(1-cosec alpha)/(1+cosec alpha)=(1-(-2))/(1+(-2))=(1+2)/(1-2)=3/-1 `
`(1-cosec alpha)/(1+cosec alpha)=-3`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Prove the following identities:
`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`
If (tan θ + sin θ) = m and (tan θ – sin θ) = n, prove that (m2 – n2)2 = 16 mn.
If `cot theta = 1/ sqrt(3) , "write the value of" ((1- cos^2 theta))/((2 -sin^2 theta))`
What is the value of (1 − cos2 θ) cosec2 θ?
What is the value of (1 + cot2 θ) sin2 θ?
Without using trigonometric table , evaluate :
`cosec49°cos41° + (tan31°)/(cot59°)`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
Prove that `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2 = 1`
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
(1 + sin A)(1 – sin A) is equal to ______.
