Advertisements
Advertisements
प्रश्न
In Given Figure, find tan P – cot R.
Advertisements
उत्तर
Applying Pythagoras theorem for ΔPQR, we obtain
PR2 = PQ2 + QR2
(13 cm)2 = (12 cm)2 + QR2
169 cm2 = 144 cm2 + QR2
25 cm2 = QR2
QR = 5 cm
tan P = `("Side opposite to ∠P")/("Side adjacent to ∠P") = ("QR")/("PQ")`
= `5/12`
cot R = `("Side opposite to ∠R")/("Side adjacent to ∠R") = ("QR")/("PQ")`
= `5/12`
tan P - cot R = `5/12 - 5/12 = 0`
APPEARS IN
संबंधित प्रश्न
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin A, cos A
State whether the following are true or false. Justify your answer.
sin θ = `4/3`, for some angle θ.
if `cot theta = 3/4` prove that `sqrt((sec theta - cosec theta)/(sec theta +cosec theta)) = 1/sqrt7`
If Cosec A = 2 find `1/(tan A) + (sin A)/(1 + cos A)`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
Evaluate the following
`2 sin^2 30^2 - 3 cos^2 45^2 + tan^2 60^@`
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Evaluate the Following:
`(tan^2 60^@ + 4 cos^2 45^@ + 3 sec^2 30^@ + 5 cos^2 90)/(cosec 30^@ + sec 60^@ - cot^2 30^@)`
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
If cos (81 + θ)° = sin`("k"/3 - theta)^circ` where θ is an acute angle, then the value of k is ______.
If sin A = `1/2`, then the value of cot A is ______.
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.
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` ......`(∵ 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)`
Find the value of sin 45° + cos 45° + tan 45°.
`sqrt(3)` cos2A + `sqrt(3)` sin2A is equal to ______.
If b = `(3 + cot π/8 + cot (11π)/24 - cot (5π)/24)`, then the value of `|bsqrt(2)|` is ______.
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
