Advertisements
Advertisements
प्रश्न
Given sec θ = `13/12`, calculate all other trigonometric ratios.
उत्तर
Let ΔABC be a right-angled triangle, right angled at point B.
It is given that:
sec θ = `"hypotenuse"/"side adjacent to ∠θ" = "AC"/"AB" = 13/12`
Let AC = 13k and AB = 12k, where k is a positive integer.
Applying pythagoras theorem in Δ ABC, we obtain:
AC2 = AB2 + BC2
BC2 = AC2 - AB2
BC2 = (13k)2 - (12k)2
BC2 = 169 k2 - 144 k2
BC2 = 25k2
BC = 5k
sin θ = `("side opposite to ∠θ")/("hypotenuse") = ("BC")/("AC") = 5/13`
cos θ = `("side adjacent to ∠θ")/("hypotenuse") = ("AB")/("AC") = 12/13`
tan θ = `("side opposite to ∠θ")/("side adjacent to ∠θ") = "(BC)"/"(AB)" = 5/12`
cot θ = `("side adjacent to ∠θ")/("side opposite to ∠θ") = ("AB")/("BC") = 12/5`
cosec θ = `("hypotenuse")/("side opposite to ∠θ") = ("AC")/("BC") = 13/5`
APPEARS IN
संबंधित प्रश्न
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
State whether the following are true or false. Justify your answer.
sin θ = `4/3`, for some angle θ.
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.
`cosec theta = sqrt10`
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 `sin theta = a/b` find sec θ + tan θ in terms of a and b.
Evaluate the Following
`cot^2 30^@ - 2 cos^2 60^circ- 3/4 sec^2 45^@ - 4 sec^2 30^@`
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Find the value of x in the following :
`sqrt3 sin x = cos x`
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.
`(sin theta)/(1 + cos theta)` is ______.
If x sin (90° – θ) cot (90° – θ) = cos (90° – θ), then x is equal to ______.
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
5 tan² A – 5 sec² A + 1 is equal to ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
The value of the expression (sin 80° – cos 80°) is negative.
If f(x) = `3cos(x + (5π)/6) - 5sinx + 2`, then maximum value of f(x) is ______.
Let tan9° = `(1 - sqrt((sqrt(5)k)/m))k` where k = `sqrt(5) + 1` then m is equal to ______.
