Advertisements
Advertisements
Question
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
Advertisements
Solution
We have ` ( sec theta + tan theta ) =m ....(i)`
Again ,` ( sec theta - tan theta ) = n .....(ii)`
Now, multiplying (i) and (ii), we get:
`(sec theta + tan theta ) xx ( sec theta - tan theta ) = mn`
` => sec^2 theta - tan^2 theta = mn `
`= > 1= mn [∵ sec^2 theta - tan^2 theta = 1 ]`
∴ mn = 1
APPEARS IN
RELATED QUESTIONS
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`tan θ/(1 - cot θ) + cot θ/(1 - tan θ) = 1 + tan θ + cot θ`
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove the following identities:
`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`
Prove that:
`cosA/(1 + sinA) = secA - tanA`
`(sec^2 theta-1) cot ^2 theta=1`
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`
If sec θ = `25/7`, find the value of tan θ.
Solution:
1 + tan2 θ = sec2 θ
∴ 1 + tan2 θ = `(25/7)^square`
∴ tan2 θ = `625/49 - square`
= `(625 - 49)/49`
= `square/49`
∴ tan θ = `square/7` ........(by taking square roots)
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`
If cos A = `(2sqrt(m))/(m + 1)`, then prove that cosec A = `(m + 1)/(m - 1)`.
Eliminate θ if x = r cosθ and y = r sinθ.
