Advertisements
Advertisements
प्रश्न
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
Advertisements
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
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
`costheta/((1-tan theta))+sin^2theta/((cos theta-sintheta))=(cos theta+ sin theta)`
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
`(sin A)/(1 + cos A) + (1 + cos A)/(sin A)` = 2 cosec A
Prove that `(tan θ)/(cot(90° - θ)) + (sec (90° - θ) sin (90° - θ))/(cosθ. cosec θ) = 2`.
Prove that sin( 90° - θ ) sin θ cot θ = cos2θ.
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove that `(cos^2θ)/(sinθ) + sin θ = "cosec" θ`.
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
Prove the following:
`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
