Advertisements
Advertisements
Question
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
Options
9
7
5
3
Advertisements
Solution
7
Explanation;
(sin α + cos α)2 + (cos α + sec α)2
= sin2α + cosec2α + 2 sin α cosec α + cos2α + sec2α + 2 cos α sec α
= 1 + cosec2α + 2 + sec2α + 2
= 1 + cot2α + 1 + 2 + tan2α + 1 + 2
= 7 + tan2α + cot2α
k = 7
APPEARS IN
RELATED QUESTIONS
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 that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`(tan theta)/((sec theta -1))+(tan theta)/((sec theta +1)) = 2 sec theta`
2 (sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) is equal to
\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
Prove the following identities.
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
