मराठी

Find the Value of Sin ` 48° Sec 42° + Cos 48° Cosec 42°` - Mathematics

Advertisements
Advertisements

प्रश्न

Find the value of sin ` 48° sec 42° + cos 48°  cosec 42°`

 

उत्तर

sin 48°  sec 42° + cos 48° cosec 42°  

=`sin 48° cosec (90 ° - 42 °) + cos 48° sec (90° - 42°)

=` sin 48° cosec 48° + cos 48° sec 48°

=` sin 48° xx 1/ (sin 48°) + cos 48° xx 1/ ( cos 48 °)`

=1  + 1

=2

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Trigonometric Identities - Exercises 3

APPEARS IN

आर एस अग्रवाल Mathematics [English] Class 10
पाठ 8 Trigonometric Identities
Exercises 3 | Q 33

संबंधित प्रश्‍न

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`


Prove the following trigonometric identities.

`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`


if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2  = 2`


Prove the following identities:

`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`


`cot^2 theta - 1/(sin^2 theta ) = -1`a


`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta` 


`sqrt((1+sin theta)/(1-sin theta)) = (sec theta + tan theta)`


`(cos  ec^theta + cot theta )/( cos ec theta - cot theta  ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta  cot theta`


`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `


`(cos theta  cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`


If `(cosec theta - sin theta )= a^3 and (sec theta - cos theta ) = b^3 , " prove that " a^2 b^2 ( a^2+ b^2 ) =1`


Write the value of `( 1- sin ^2 theta  ) sec^2 theta.`


If \[\sin \theta = \frac{1}{3}\] then find the value of 9tan2 θ + 9. 


Prove the following identity : 

`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`


Prove the following identity : 

`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`


If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.


Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.


If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.


Prove the following:

`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ


If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×