Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
If sin A = `3/4`, calculate cos A and tan A.
If cot θ = `7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`.
State whether the following are true or false. Justify your answer.
cot A is the product of cot and A.
If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos A = 4/5`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cos theta = 12/2`
If `tan theta = 1/sqrt7` `(cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta) = 3/4`
if `sec A = 17/8` verify that `(3 - 4sin^2A)/(4 cos^2 A - 3) = (3 - tan^2 A)/(1 - 3 tan^2 A)`
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
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°
Find the value of x in the following :
`sqrt3 sin x = cos x`
If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.
If cos (81 + θ)° = sin`("k"/3 - theta)^circ` where θ is an acute angle, then the value of k is ______.
A ladder rests against a vertical wall at an inclination α to the horizontal. Its foot is pulled away from the wall through a distance p so that its upper end slides a distance q down the wall and then the ladder makes an angle β to the horizontal. Show that `p/q = (cos β - cos α)/(sin α - sin β)`
If cosec θ = `("p" + "q")/("p" - "q")` (p ≠ q ≠ 0), then `|cot(π/4 + θ/2)|` is equal to ______.
In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.
Evaluate: 5 cosec2 45° – 3 sin2 90° + 5 cos 0°.
