Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If Cosec A = 2 find `1/(tan A) + (sin A)/(1 + cos A)`
Advertisements
рдЙрддреНрддрд░
`Cosec A = "hypotenuse"/"opposite side" = 2/1`
Let x be the adjacent side
By applying Pythagoras theorem
`AC^2 = AB^2 + BC^2`
4 = 1 + ЁЭСе2
`x^2 = 3 => x = sqrt3`
`sin A = 1/(cosec A) = 1/2`
`tan A = (AB)/(BC) = 1/sqrt3`
`cos A = (BC)/(AC) = sqrt3/2`
Substitute in equation we get
`1/tan A + sin A /(1+ cos A) = 1/(1/sqrt3) + (1/2)/(1 + sqrt3/2)`
`=> sqrt3 + (1/2)/((2 + sqrt3)/2) = sqrt3 + 1/(2 + sqrt3) = (2sqrt3 + 3 +1)/(2 + sqrt3) = (2sqrt3 + 4)/(2 + sqrt3) = (2(2 + sqrt3))/(2 + sqrt3) = 2`
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin A = 2/3`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
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 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 `cot theta = 1/sqrt3` show that `(1 - cos^2 theta)/(2 - sin^2 theta) = 3/5`
if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`
if `sin theta = 3/4` prove that `sqrt(cosec^2 theta - cot)/(sec^2 theta - 1) = sqrt7/3`
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Evaluate the Following
`cot^2 30^@ - 2 cos^2 60^circ- 3/4 sec^2 45^@ - 4 sec^2 30^@`
Find the value of x in the following :
`2sin 3x = sqrt3`
Find the value of x in the following :
`2 sin x/2 = 1`
If sin (A − B) = sin A cos B − cos A sin B and cos (A − B) = cos A cos B + sin A sin B, find the values of sin 15° and cos 15°.
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 sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
If sin A = `1/2`, then the value of cot A is ______.
In the given figure, if sin θ = `7/13`, which angle will be θ?
Prove that `tan θ/(1 - cot θ) + cot θ/(1 - tanθ)` = 1 + sec θ cosec θ
If θ is an acute angle of a right angled triangle, then which of the following equation is not true?
