Question

निम्नलखित समीकरणों को हल कीजिए -
(i) `sec^(2) .theta/2 = 2 sqrt2tan theta//2" "(0^(@) lt thetalt 360^(@))`
(ii) `cos 2theta-sin2 theta=costheta-sintheta-1" "(90^(@) lt thetalt 540^(@))`
(iii)`cos theta+sec theta = 5/2" "(3pi lt thetalt 5pi)`
(iv) `sin 3 theta +sin 2 theta +sin theta =0" "(0^(@) lt theta lt 360^(@))`
(v) `4 cos^(2) theta +sqrt3 = 2 (sqrt3+1) cos theta`

Answer 1

Correct Answer - (i) `45^(@), 135^(@) " "(ii)225^(@), 300^(@), 405^(@), 420^(@)" " (iii) 4pi + pi/3" " (iv) 90^(@), 180^(@), 270^(@), 120^(@), 240^(@)" " (v) 2n pi pm pi/3, 2n pi pm pi/6`
(i)` sec^(2) theta//2 = 2 sqrt2 tan . theta/2 rArr 2 sqrt2 sin . theta/2 cos. theta/2 = 1`
`rArr2 sin . theta/2 cos. theta/2 = 1/sqrt2`
`rArr sin theta = sin 45^(@) "या " sin 135^(@)`
`rArr theta = 45^(@) , 135^(@)`