Advertisements
Advertisements
Question
Prove that sec θ + tan θ = `cos θ/(1 - sin θ)`.
Proof: L.H.S. = sec θ + tan θ
= `1/square + square/square`
= `square/square` ......`(∵ sec θ = 1/square, tan θ = square/square)`
= `((1 + sin θ) square)/(cos θ square)` ......[Multiplying `square` with the numerator and denominator]
= `(1^2 - square)/(cos θ square)`
= `square/(cos θ square)`
= `cos θ/(1 - sin θ)` = R.H.S.
∴ L.H.S. = R.H.S.
∴ sec θ + tan θ = `cos θ/(1 - sin θ)`
Advertisements
Solution
Proof: L.H.S. = sec θ + tan θ
= `1/bb(cos θ) + bb(sin θ)/bb(cos θ)` ........`[∵ sec θ = 1/bb(cos θ), tan θ = bb(sin θ)/bb(cos θ)]`
= `bb(1 + sintheta)/bbcostheta` = `((1 + sin θ) bb(1 - sin θ))/(cos θ bb(1 - sin θ)` ......[Multiplying `bb(1 - sin θ)` with the numerator and denominator]
= `(1^2 - bb(sin^2 θ))/(cos θ bb(1 - sin θ)`
= `bb (cos^2 θ)/(cos θ bb(1 - sin θ)`
= `cos θ/(1 - sin θ)` = R.H.S.
∴ L.H.S. = R.H.S.
∴ sec θ + tan θ = `cos θ/(1 - sin θ)`
APPEARS IN
RELATED QUESTIONS
If cot θ = `7/8`, evaluate cot2 θ.
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cot theta = 12/5`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
If `tan theta = a/b`, find the value of `(cos theta + sin theta)/(cos theta - sin theta)`
If `cot theta = 1/sqrt3` show that `(1 - cos^2 theta)/(2 - sin^2 theta) = 3/5`
If `tan theta = 24/7`, find that sin θ + cos θ.
if `sin theta = 3/4` prove that `sqrt(cosec^2 theta - cot)/(sec^2 theta - 1) = sqrt7/3`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Find the value of x in each of the following :
cos x = cos 60º cos 30º + sin 60º sin 30º
If sin (A − B) = sin A cos B − cos A sin B and cos (A − B) = cos A cos B + sin A sin B, find the values of sin 15° and cos 15°.
sin (45° + θ) – cos (45° – θ) is equal to ______.
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
The value of the expression `[(sin^2 22^circ + sin^2 68^circ)/(cos^2 22^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin 27^circ]` is ______.
What will be the value of sin 45° + `1/sqrt(2)`?
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
If f(x) = `3cos(x + (5π)/6) - 5sinx + 2`, then maximum value of f(x) is ______.
If θ is an acute angle of a right angled triangle, then which of the following equation is not true?
