Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If `tan theta = 1/sqrt7` `(cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta) = 3/4`
Advertisements
рдЙрддреНрддрд░
`tan theta = 1/sqrt7` `(cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta) = 3/4`
`tan theta = "ЁЭСЬЁЭСЭЁЭСЭЁЭСЬЁЭСаЁЭСЦЁЭСбЁЭСТ ЁЭСаЁЭСЦЁЭССЁЭСТ"/"ЁЭСОЁЭССЁЭСЧЁЭСОЁЭСРЁЭСТЁЭСЫЁЭСб ЁЭСаЁЭСЦЁЭССЁЭСТ"`
Let ‘x’ be the hypotenuse
By applying Pythagoras
ЁЭР┤ЁЭР╢2 = ЁЭР┤ЁЭР╡2 + ЁЭР╡ЁЭР╢2
`x^2 = 1^2 + (sqrt7)^2`
ЁЭСе2 = 1 + 7 = 8
`x = 2sqrt2`
`cosec theta = (AC)/(AB) = 2sqrt2`
`sec theta = (AC)/(BC) = (2sqrt2)/sqrt7`
Substitute, cosec θ, sec θ in equation
`=> ((2sqrt2)^2 - (2 sqrt(2/7))^2)/((2sqrt2)^2 + ((2sqrt2)/sqrt7)^2)`
`(8 - 4 xx 2/7)/(8 + 4 xx 2/7)`
`=> (8 - 8/7)/(8 + 8/7)`
`=> ((56 - 8)/7)/((56 + 8)/7)`
`=48/64`
`= 3/4`
L.H.S = R.H.S
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
State whether the following are true or false. Justify your answer.
cos A is the abbreviation used for the cosecant of angle A.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos A = 4/5`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cos theta = 12/2`
If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`
If `tan theta = 24/7`, find that sin θ + cos θ.
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
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
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
Find the value of x in the following :
`sqrt3 sin x = cos x`
The value of sin² 30° – cos² 30° is ______.
If cos A = `4/5`, then the value of tan A is ______.
Find the value of sin 0° + cos 0° + tan 0° + sec 0°.
`sqrt(3)` cos2A + `sqrt(3)` sin2A is equal to ______.
If f(x) = `3cos(x + (5π)/6) - 5sinx + 2`, then maximum value of f(x) is ______.
The maximum value of the expression 5cosα + 12sinα – 8 is equal to ______.
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
