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
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin C, cos C
State whether the following are true or false. Justify your answer.
sin θ = `4/3`, for some angle θ.
If 3 cot θ = 2, find the value of `(4sin theta - 3 cos theta)/(2 sin theta + 6cos theta)`.
If `tan theta = 24/7`, find that sin θ + cos θ.
Evaluate the Following
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45°
Evaluate the Following
`cot^2 30^@ - 2 cos^2 60^circ- 3/4 sec^2 45^@ - 4 sec^2 30^@`
Evaluate the Following
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@`
Find the value of x in each of the following :
cos x = cos 60º cos 30º + sin 60º sin 30º
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
The value of sin² 30° – cos² 30° is ______.
If cos (81 + θ)° = sin`("k"/3 - theta)^circ` where θ is an acute angle, then the value of k is ______.
The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is ______.
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
A ladder rests against a vertical wall at an inclination α to the horizontal. Its foot is pulled away from the wall through a distance p so that its upper end slides a distance q down the wall and then the ladder makes an angle β to the horizontal. Show that `p/q = (cos β - cos α)/(sin α - sin β)`
In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
Let f(x) = sinx.cos3x and g(x) = cosx.sin3x, then the value of `7((f(π/7) + g(π/7))/(g((5π)/14) + f((5π)/14)))` is ______.
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
