English

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

Advertisements
Advertisements

Question

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

 

Solution

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
  Is there an error in this question or solution?
Chapter 8: Trigonometric Identities - Exercises 3

APPEARS IN

RS Aggarwal Mathematics [English] Class 10
Chapter 8 Trigonometric Identities
Exercises 3 | Q 33

RELATED QUESTIONS

Prove the following trigonometric identities:

(i) (1 – sin2θ) sec2θ = 1

(ii) cos2θ (1 + tan2θ) = 1


Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`

 


Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 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

cosec6θ = cot6θ + 3 cot2θ cosec2θ + 1


Prove the following trigonometric identities.

`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`


If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.


Prove the following identities:

cot2 A – cos2 A = cos2 A . cot2 A


Prove the following identities:

`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`


Prove the following identities:

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


`(1 + cot^2 theta ) sin^2 theta =1`


`sin^2 theta + 1/((1+tan^2 theta))=1`


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


Write True' or False' and justify your answer the following: 

\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.


If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.


Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`


If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1


If 1 – cos2θ = `1/4`, then θ = ?


Prove the following:

`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A


If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×