Advertisements
Advertisements
рдкреНрд░рд╢реНрди
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
Advertisements
рдЙрддреНрддрд░
We have ,
5 `tan theta = 4`
⇒ `tan theta = 4/5`
Now ,
`((cos theta - sintheta))/(( cos theta + sin theta))`
`=(((cos theta )/(cos theta)- (sin theta )/(cos theta)))/((cos theta/ cos theta+ sin theta/ cos theta)` (ЁЭР╖ЁЭСЦЁЭСгЁЭСЦЁЭССЁЭСЦЁЭСЫЁЭСФ ЁЭСЫЁЭСвЁЭСЪЁЭСТЁЭСЯЁЭСОЁЭСбЁЭСЬЁЭСЯ ЁЭСОЁЭСЫЁЭСС ЁЭССЁЭСТЁЭСЫЁЭСЬЁЭСЪЁЭСЦЁЭСЫЁЭСОЁЭСбЁЭСЬЁЭСЯ ЁЭСПЁЭСж cos θ)
`=((1- tan theta))/((1+ tan theta))`
`= ((1/1-4/5))/((1/1+4/5))`
`= ((1/5))/((9/5))`
`= 1/9`
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
Express the ratios cos A, tan A and sec A in terms of sin A.
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Prove the following trigonometric identities.
tan2 θ − sin2 θ = tan2 θ sin2 θ
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
`(1-cos^2theta) sec^2 theta = tan^2 theta`
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
Write the value of`(tan^2 theta - sec^2 theta)/(cot^2 theta - cosec^2 theta)`
If sec θ + tan θ = x, then sec θ =
cos4 A − sin4 A is equal to ______.
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
If sin θ − cos θ = 0 then the value of sin4θ + cos4θ
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
Prove that `(tan θ)/(cot(90° - θ)) + (sec (90° - θ) sin (90° - θ))/(cosθ. cosec θ) = 2`.
