Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
tan (90 – θ) = ?
पर्याय
sin θ
cos θ
cot θ
tan θ
Advertisements
उत्तर
cot θ
APPEARS IN
संबंधित प्रश्न
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
`(1-cos^2theta) sec^2 theta = tan^2 theta`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
`(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
\[\frac{x^2 - 1}{2x}\] is equal to
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove the following identity :
`(1 + tan^2θ)sinθcosθ = tanθ`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
If a sinθ + b cosθ = c, then prove that a cosθ – b sinθ = `sqrt(a^2 + b^2 - c^2)`.
Find the value of sin2θ + cos2θ

Solution:
In Δ ABC, ∠ABC = 90°, ∠C = θ°
AB2 + BC2 = `square` .....(Pythagoras theorem)
Divide both sides by AC2
`"AB"^2/"AC"^2 + "BC"^2/"AC"^2 = "AC"^2/"AC"^2`
∴ `("AB"^2/"AC"^2) + ("BC"^2/"AC"^2) = 1`
But `"AB"/"AC" = square and "BC"/"AC" = square`
∴ `sin^2 theta + cos^2 theta = square`
