Advertisements
Advertisements
प्रश्न
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
Advertisements
उत्तर
LHS = `cos theta/((1-tan theta))-sin^2theta/((cos theta-sintheta))`
=`cos theta/((1-sintheta/costheta)) -sin^2 theta/((cos theta-sin theta))`
=`cos^2 theta/((cos theta-sintheta))- sin^2 theta/((cos theta-sin theta))`
=`(cos^2 theta- sin ^2 theta)/((cos theta- sin theta))`
=`((costheta + sin theta)( cos theta-sin theta))/((cos theta - sin theta))`
=`(cos theta + sin theta)`
= RHS
Hence, LHS = RHS
APPEARS IN
संबंधित प्रश्न
(secA + tanA) (1 − sinA) = ______.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
As observed from the top of an 80 m tall lighthouse, the angles of depression of two ships on the same side of the lighthouse of the horizontal line with its base are 30° and 40° respectively. Find the distance between the two ships. Give your answer correct to the nearest meter.
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
Prove that
`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`
`1+ (cot^2 theta)/((1+ cosec theta))= cosec theta`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove that `sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A - 1) = 1`.
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S = `square`
= `cos^2theta xx square .....[1 + tan^2theta = square]`
= `(cos theta xx square)^2`
= 12
= 1
= R.H.S
Prove that sin6A + cos6A = 1 – 3sin2A . cos2A
