Advertisements
Advertisements
प्रश्न
Prove that cot2θ × sec2θ = cot2θ + 1.
Advertisements
उत्तर
L.H.S. = cot2θ × sec2θ
= `(cos^2θ)/(sin^2θ) xx 1/(cos^2θ)`
= `1/(sin^2θ)`
= cosec2θ
= 1 + cot2θ ...[∵ 1 + cot2θ = cosec2θ]
= R.H.S.
∴ cot2θ × sec2θ = cot2θ + 1
APPEARS IN
संबंधित प्रश्न
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.
Prove the following identities:
`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`
`(sec theta -1 )/( sec theta +1) = ( sin ^2 theta)/( (1+ cos theta )^2)`
`{1/((sec^2 theta- cos^2 theta))+ 1/((cosec^2 theta - sin^2 theta))} ( sin^2 theta cos^2 theta) = (1- sin^2 theta cos ^2 theta)/(2+ sin^2 theta cos^2 theta)`
Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50° cosec 40 °`
If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`
Find the value of `(cos 38° cosec 52°)/(tan 18° tan 35° tan 60° tan 72° tan 55°)`
If sin θ − cos θ = 0 then the value of sin4θ + cos4θ
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove the following Identities :
`(cosecA)/(cotA+tanA)=cosA`
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
sec2θ – tan2θ = ?
Prove that `"cosec" θ xx sqrt(1 - cos^2θ) = 1`.
tan2θ – sin2θ = tan2θ × sin2θ. For proof of this complete the activity given below.
Activity:
L.H.S. = `square`
= `square (1 - (sin^2θ)/(tan^2θ))`
= `tan^2θ (1 - square/((sin^2θ)/(cos^2θ)))`
= `tan^2θ (1 - (sin^2θ)/1 xx (cos^2θ)/square)`
= `tan^2θ (1 - square)`
= `tan^2θ xx square` ...[1 – cos2θ = sin2θ]
= R.H.S.
Prove that sin4A – cos4A = 1 – 2 cos2A.
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
