Advertisements
Advertisements
рдкреНрд░рд╢реНрди
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
Advertisements
рдЙрддреНрддрд░
consider a right-angled Δle ABC, we get
Let x be the adjacent side.
By applying Pythagoras theorem
ЁЭР┤ЁЭР╢2 = ЁЭР┤ЁЭР╡2 + ЁЭР╡ЁЭР╢2
`(sqrt10)^2 = 1^2 + x^2`
x2 = 10 − 1 = 9
x = 3
`sin theta = 1/cosec theta = 1/sqrt10`
`cos theta = "adjacent"/"hypotenuse" = 3/sqrt10`
`tan theta = "opposite sides"/"adjacebt side" = 1/3`
`sec theta = 1/cos theta = sqrt10/3`
`cot theta = 1/tan theta = (1/1)/3 = 3`
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = 11/5`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
If `cos θ = 12/13`, show that `sin θ (1 - tan θ) = 35/156`.
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 ЁЭЬГ + cos ЁЭЬГ
if `sin theta = 3/4` prove that `sqrt(cosec^2 theta - cot)/(sec^2 theta - 1) = sqrt7/3`
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 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 cos (40° + A) = sin 30°, then value of A is ______.
`(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 ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
Find the value of sin 45° + cos 45° + tan 45°.
If sec θ = `1/2`, what will be the value of cos θ?
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
If θ is an acute angle of a right angled triangle, then which of the following equation is not true?
If sin θ – cos θ = 0, then find the value of sin4 θ + cos4 θ.
