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
In Given Figure, find tan P – cot R.
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan alpha = 5/12`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`
If `tan θ = a/b` then prove that `((a sin theta - b cos theta)/(a sin theta + b cos theta)) = ((a^2 - b^2))/((a^2 + b^2))`.
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 θ = 3/4` prove that `sqrt(("cosec"^2θ - cot^2θ)/(sec^2θ - 1)) = sqrt(7)/3`.
Evaluate the following
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`
Evaluate the Following
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60°
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
sin (45° + θ) – cos (45° – θ) is equal to ______.
If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to ______.
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
If sin θ + cos θ = `sqrt(2)` then tan θ + cot θ = ______.
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
In a right triangle PQR, right angled at Q. If tan P = `sqrt(3)`, then evaluate 2 sin P cos P.
