Advertisements
Advertisements
Question
Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[∵ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
Advertisements
Solution
Proof: L.H.S. = cot θ + tan θ
= `bbcos θ/bbsin θ + bbsin θ/bbcos θ` ......`[∵ cot θ = bbcos θ/bbsin θ, tan θ = bb sinθ/bbcos θ]`
= `(bb(cos^2θ) + bb(sin^2θ))/(bbsin θ xx bbcos θ)` .....`[∵ bb(cos^2θ) + bb(sin^2θ) = 1]`
= `1/(bb sin θ xx bb cos θ)`
= `1/bb sin θ xx 1/bb cos θ`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/bb sin θ, sec θ = 1/bb cos θ]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
APPEARS IN
RELATED QUESTIONS
If sin A = `3/4`, calculate cos A and tan A.
Given sec θ = `13/12`, calculate all other trigonometric ratios.
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
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.
`tan theta = 8/15`
If `cot theta = 1/sqrt3` show that `(1 - cos^2 theta)/(2 - sin^2 theta) = 3/5`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
If `tan theta = 24/7`, find that sin θ + cos θ.
Find the value of x in the following :
`sqrt3 tan 2x = cos 60^@ + sin45^@ cos 45^@`
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
5 tan² A – 5 sec² A + 1 is equal to ______.
The value of the expression `[(sin^2 22^circ + sin^2 68^circ)/(cos^2 22^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin 27^circ]` is ______.
The value of the expression (sin 80° – cos 80°) is negative.
`sqrt(3)` cos2A + `sqrt(3)` sin2A is equal to ______.
Prove that `tan θ/(1 - cot θ) + cot θ/(1 - tanθ)` = 1 + sec θ cosec θ
If sin θ + cos θ = `sqrt(2)` then tan θ + cot θ = ______.
If cos(α + β) = `(3/5)`, sin(α – β) = `5/13` and 0 < α, β < `π/4`, then tan (2α) is equal to ______.
If f(x) = `3cos(x + (5π)/6) - 5sinx + 2`, then maximum value of f(x) is ______.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.
