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
In Given Figure, find tan P – cot R.
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin A = 2/3`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
If `sin theta = a/b` find sec θ + tan θ in terms of a and b.
Evaluate the following
cos 60° cos 45° - sin 60° ∙ sin 45°
Evaluate the Following
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45°
Evaluate the Following
`sin 30^2/sin 45^@ + tan 45^@/sec 60^@ - sin 60^@/cot 45^@ - cos 30^@/sin 90^@`
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
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.
In the given figure, if sin θ = `7/13`, which angle will be θ?
Find will be the value of cos 90° + sin 90°.
