Advertisements
Advertisements
प्रश्न
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
विकल्प
0
1
sin θ + cos θ
sin θ − cos θ
उत्तर
The given expression is ` sin θ/(1-cot θ)+ cos θ/(1-tan θ)`
Simplifying the given expression, we have
`sin θ/(1-cot θ)+ cos θ/(1-tan θ)`
= `sinθ/(1-cosθ/sinθ)+cos θ/(1-sinθ/cos θ)`
=` sin θ/((sinθ-cos θ)/sin θ)+cos θ/((cos θ-sin θ)/cos θ)`
= `sin^2θ/(sin θ-cos θ)+cos^2θ/(cos θ-sin θ)`
= `sin^2θ/(sin θ-cos θ)+cos ^2θ/(-1(sin θ-cos θ))`
= `sin ^2θ/(sin θ-cos θ)-cos ^2 θ/(sin θ-cos θ)`
= `(sin^2θ-cos^2θ)/(sin θ-cos θ)`
=` ((sinθ+cos θ)(sinθ-cos θ))/(sin θ-cos θ)`
=` sin θ+cos θ`
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 trigonometric identities.
`tan A/(1 + tan^2 A)^2 + cot A/((1 + cot^2 A)) = sin A cos A`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`
Prove that:
cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A
If `cot theta = 1/ sqrt(3) , "write the value of" ((1- cos^2 theta))/((2 -sin^2 theta))`
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
The value of sin2 29° + sin2 61° is
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
`tan^2A - sin^2A = tan^2A.sin^2A`
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Prove that:
tan (55° + x) = cot (35° – x)
Prove that `((1 + sin θ - cos θ)/( 1 + sin θ + cos θ))^2 = (1 - cos θ)/(1 + cos θ)`.
tan θ cosec2 θ – tan θ is equal to
Prove that `sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ
If tan θ – sin2θ = cos2θ, then show that sin2 θ = `1/2`.
If tan θ = `x/y`, then cos θ is equal to ______.
(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.
