Advertisements
Advertisements
प्रश्न
If `tan theta = a/b`, find the value of `(cos theta + sin theta)/(cos theta - sin theta)`
Advertisements
उत्तर
tan theta = a/b find `(cos theta + sin theta)/(cos theta - sin theta)` ....(i)
Divide equation (i) with cos θ, we get
`=> ((cos theta + sin theta)/cos theta)/((cos theta - sin theta)/cos theta)`
`=> (1 + sin theta/cos theta)/(1 - sin theta/cos theta)`
`=> (1 + tan theta)/(1 - tan theta)`
`= (1+ a/b)/(1 - a/b)`
`= (b + a)/(b - a)`
APPEARS IN
संबंधित प्रश्न
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin A, cos A
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
Prove that `(sin "A" - 2sin^3 "A")/(2cos^3 "A" - cos "A") = tan "A"`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos A = 4/5`
If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`
If 3 cot θ = 2, find the value of `(4sin theta - 3 cos theta)/(2 sin theta + 6cos theta)`.
If tan θ = `a/b` prove that `(a sin theta - b cos theta)/(a sin theta + b cos theta) = (a^2 - b^2)/(a^2 + b^2)`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
if `cot theta = 3/4` prove that `sqrt((sec theta - cosec theta)/(sec theta +cosec theta)) = 1/sqrt7`
If `tan theta = 24/7`, find that sin 𝜃 + cos 𝜃
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
If Cosec A = 2 find `1/(tan A) + (sin A)/(1 + cos A)`
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
If sin 2A = `1/2` tan² 45° where A is an acute angle, then the value of A is ______.
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 ______.
Prove the following:
If tan A = `3/4`, then sinA cosA = `12/25`
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)`
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
If cosec θ = `("p" + "q")/("p" - "q")` (p ≠ q ≠ 0), then `|cot(π/4 + θ/2)|` is equal to ______.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
