Advertisements
Advertisements
Question
Prove that: `((cot30° + 1)/(cot30° -1))^2 = (sec30° + 1)/(sec30° - 1)`
Solution
L.H.S. = `((cot30° + 1)/(cot30° -1))^2`
= `((sqrt(3) + 1)/(sqrt(3) - 1))^2`
= `((sqrt(3) + 1)/(sqrt(3) - 1) xx (sqrt(3) + 1)/(sqrt(3) + 1))^2`
= `((sqrt(3))^2 + (1)^2 + 2sqrt(3))/((sqrt(3))^2 + (1)^2 - 2sqrt(3)`
= `(3 + 1 + 2sqrt(3))/(3 + 1 - 2sqrt(3)`
= `(4 + 2sqrt(3))/(4 - 2sqrt(3)`
= `(2(2 + sqrt(3)))/(2(2 - sqrt(3))`
= `(2 + sqrt(3))/(2 - sqrt(3)`
= `(2/sqrt(3) + 1)/(2/sqrt(3) - 1)`
= `(sec30° + 1)/(sec30° - 1)`
= R.H.S.
APPEARS IN
RELATED QUESTIONS
If θ is an acute angle and sin θ = cos θ, find the value of 2 tan2 θ + sin2 θ – 1
An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.
`(2 tan 30°)/(1-tan^2 30°)` = ______.
State whether the following is true or false. Justify your answer.
sinθ = cosθ for all values of θ.
Evaluate the following :
`(sin 21^@)/(cos 69^@)`
Evaluate the following :
sin 35° sin 55° − cos 35° cos 55°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
cos 78° + sec 78°
Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°
sin 67° + cos 75°
If Sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A =?
Prove the following :
`(cos(90°−A) sin(90°−A))/tan(90°−A) - sin^2 A = 0`
Evaluate:
`2/3 (cos^4 30° - sin^4 45°) - 3(sin^2 60° - sec^2 45°) + 1/4 cot^2 30°`.
prove that:
sin (2 × 30°) = `(2 tan 30°)/(1+tan^2 30°)`
If A = 30°;
show that:
sin 3 A = 4 sin A sin (60° - A) sin (60° + A)
find the value of: cosec2 60° - tan2 30°
find the value of: sin2 30° + cos2 30°+ cot2 45°
secθ . Cot θ= cosecθ ; write true or false
For any angle θ, state the value of: sin2 θ + cos2 θ
If `sqrt3` = 1.732, find (correct to two decimal place) the value of `(2)/(tan 30°)`
If A =30o, then prove that :
cos 2A = cos2A - sin2A = `(1 – tan^2"A")/(1+ tan^2"A")`
If A = 30o, then prove that :
2 cos2 A - 1 = 1 - 2 sin2A
If A = 30°;
show that:
`(1 + sin 2"A" + cos 2"A")/(sin "A" + cos"A") = 2 cos "A"`
Without using tables, evaluate the following: cosec245° sec230° - sin230° - 4cot245° + sec260°.
Without using tables, evaluate the following: cosec330° cos60° tan345° sin290° sec245° cot30°.
Find the value of x in the following: `sqrt(3)sin x` = cos x
If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.
If 2 sin 2θ = `sqrt(3)` then the value of θ is
Prove the following:
`(sqrt(3) + 1) (3 - cot 30^circ)` = tan3 60° – 2 sin 60°
Find the value of x if `2 "cosec"^2 30 + x sin^2 60 - 3/4 tan^2 30` = 10
