Advertisements
Advertisements
Question
Without using trigonometric tables evaluate
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`
Advertisements
Solution
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80)`
`= (sin 35^@ . cos (90^@ - 35^@) + cos 35^@. sin (90^@ - 35^@))/(cosec^2(90^@ - 80^@) - tan^2 80^@`)
`= (sin 35^@ . sin 35^@ + cos 35^@ . cos 35^@) /(sec^2 80^@ - tan^2 80^@)`
`= (sin^2 35^@ + cos^2 35^@)/(sec^2 80^@ - tan^2 80^@) = 1/1 = 1`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
Show that : tan 10° tan 15° tan 75° tan 80° = 1
If tan A = n tan B and sin A = m sin B , prove that `cos^2 A = ((m^2-1))/((n^2 - 1))`
Write the value of cosec2 (90° − θ) − tan2 θ.
If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ?
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
