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рдкреНрд░рд╢реНрди
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = 11/5`
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рдЙрддреНрддрд░
We know `sin theta = "opposite side"/"hypotenuse" = 11/15`
Consider right-angled Δle ACB
Let x = ЁЭСОЁЭССЁЭСЧЁЭСОЁЭСРЁЭСТЁЭСЫЁЭСб ЁЭСаЁЭСЦЁЭССЁЭСТ
By applying Pythagoras
ЁЭР┤ЁЭР╡2 = ЁЭР┤ЁЭР╢2 + ЁЭР╡ЁЭР╢2
225 = 121+ЁЭСе2
ЁЭСе2 = 225 -121
ЁЭСе2 = 104
`x = sqrt104`
`cos = "adjacent side"/"hypotenuse" = sqrt(104/15)`
`tan = "opposite side"/"adjacent side" = 11/sqrt104`
`cosec theta = 1/sin theta = 15/11`
`sec = 1/cos theta = 15/sqrt104`
`cot = 1/ tan theta = sqrt104/11`
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рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
State whether the following are true or false. Justify your answer.
sec A = `12/5` for some value of angle A.
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
If `cos θ = 12/13`, show that `sin θ (1 - tan θ) = 35/156`.
if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`
if `cos theta = 3/5`, find the value of `(sin theta - 1/(tan theta))/(2 tan theta)`
if `cot theta = 3/4` prove that `sqrt((sec theta - cosec theta)/(sec theta +cosec theta)) = 1/sqrt7`
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
The value of sin² 30° – cos² 30° is ______.
5 tan² A – 5 sec² A + 1 is equal to ______.
If sin A = `1/2`, then the value of cot A is ______.
Prove that sec θ + tan θ = `cos θ/(1 - sin θ)`.
Proof: L.H.S. = sec θ + tan θ
= `1/square + square/square`
= `square/square` ......`(тИ╡ sec θ = 1/square, tan θ = square/square)`
= `((1 + sin θ) square)/(cos θ square)` ......[Multiplying `square` with the numerator and denominator]
= `(1^2 - square)/(cos θ square)`
= `square/(cos θ square)`
= `cos θ/(1 - sin θ)` = R.H.S.
∴ L.H.S. = R.H.S.
∴ sec θ + tan θ = `cos θ/(1 - sin θ)`
What will be the value of sin 45° + `1/sqrt(2)`?
Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[тИ╡ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[тИ╡ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[тИ╡ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
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 cosec θ = `("p" + "q")/("p" - "q")` (p ≠ q ≠ 0), then `|cot(π/4 + θ/2)|` is equal to ______.
(3 sin2 30° – 4 cos2 60°) is equal to ______.
