Question

sin2 85° + sin2 80° + sin2 10° + sin2 5° =2​

Answer 1

Answer:

1/2

Step-by-step explanation:

sin (85+80+10+5)

sin 180

sin 150+30

sin 30

1/2

Answer 2

${ \tt{ \large{Question \colon}}}$

${ \rm{ {sin}^{2}85° + {sin}^{2} 80° + {sin}^{2}10°+{sin}^{2}5° = 2}}$

${ \tt{ \large{Solution \colon}}}$

${ \rm{ {sin}^{2}85° + {sin}^{2} 80° + {sin}^{2}10°</p><p>+{sin}^{2}5° = 2}}$

${ \rm{ = {sin}^{2} 85° + {sin}^{2}5° + {sin}^{2}80° + {sin}^{2} 10° }}$

${ \rm{ = {sin}^{2} 85° + {sin}^{2}(90° - 85°) + {sin}^{2}80° + {sin}^{2} (90° - 80°)}}$

${ \rm{ = {sin}^{2} 85° + {cos}^{2}85° + {sin}^{2}80° + {cos}^{2} 80°}}$

${ \rm{ = ({sin}^{2} 85° + {cos}^{2}85° )+ ({sin}^{2}80° + {cos}^{2} 80°)}}$

${ \rm{ = 1 + 1 = 2}}$

${\rm{ \therefore L.H.S. = R.H.S.}}$

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${ \rm{(i) {sin}^{2} \theta + {cos}^{2} \theta = 1}}$

${ \rm{(ii) {sec}^{2} \theta - {tan}^{2} \theta = 1}}$

${ \rm{(iii) {cosec}^{2} \theta - {cot}^{2} \theta = 1}}$