Advertisements
Advertisements
प्रश्न
In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.
Advertisements
उत्तर
Given that, PR + QR = 25
PQ = 5
Let PR be x.
Therefore, QR = 25 − x
Applying Pythagoras theorem in ΔPQR, we obtain
PR2 = PQ2 + QR2
x2 = (5)2 + (25 − x)2
x2 = 25 + 625 + x2 − 50x
50x = 650
x = 13
Therefore, PR = 13 cm
QR = (25 − 13) cm
= 12 cm
sin P = `("QR")/("PR")=12/13`
cos P = `("PQ")/("PR")=5/13`
tan P = `("QR")/("PQ")=12/5`
APPEARS IN
संबंधित प्रश्न
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin A, cos A
If cot θ =` 7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`
State whether the following are true or false. Justify your answer.
sin θ = `4/3`, for some angle θ.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos A = 4/5`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan alpha = 5/12`
If tan θ = `a/b` prove that `(a sin theta - b cos theta)/(a sin theta + b cos theta) = (a^2 - b^2)/(a^2 + b^2)`
if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
Evaluate the following
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`
Evaluate the Following
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45°
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Find the value of x in the following :
`2sin 3x = sqrt3`
The value of sin² 30° – cos² 30° is ______.
`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.
Given that sinα = `1/2` and cosβ = `1/2`, then the value of (α + β) is ______.
In the given figure, if sin θ = `7/13`, which angle will be θ?
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
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
