Question

sin2 35° + sin2 55°
​

Answer 1

Answer:

1

Step-by-step explanation:

In trigonometry:

    sin(90 - A) = cosA

So, here, sin²35 = sin²(90 - 55)

                           = cos²55

Therefore,

⇒ sin²35 + sin²55

⇒ cos²55 + sin²55

⇒ 1                   { sin²A + cos²A =1}

Answer 2

${ \tt{ \large \underline{question \colon}}}$

${ \rm{ {sin}^{2} 35 \degree + {sin}^{2} 55 \degree}}$

${ \tt{ \large \underline{to \: find \colon}}}$

${ \rm{ { \tt{ \longrightarrow the \: value \: of}} \: {sin}^{2} 35 \degree + {sin}^{2} 55 \degree}}$

${ \tt{ \large \underline{solution \colon}}}$

${ \rm{ {sin}^{2} 35 \degree + {sin}^{2} 55 \degree}}$

${ \rm{ = {sin}^{2} 35 \degree + {sin}^{2} 55 \degree}}$

${ \rm{ = {sin}^{2} 35 \degree + {sin}^{2} (90 \degree - 35 \degree)}}$

${ \rm{ = {sin}^{2} 35 \degree + {cos}^{2} 35 \degree}}$

${ \rm{ = 1}}$

${ \rm{ so \: the \: value \: of \: {sin}^{2} 35 \degree + {sin}^{2} 55 \degree \: is = 1}}$

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${ \tt{ \large \underline{more \: info \colon}}}$

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

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

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

${ \rm{1. \: sin( 90 \degree - \theta) = cos \theta}}$

${ \rm{2. \: cos( 90 \degree - \theta) = sin \theta}}$

${ \rm{3. \: tan( 90 \degree - \theta) = cot\theta}}$

${ \rm{4. \: sec( 90 \degree - \theta) = cosec\theta}}$

${ \rm{5. \: cosec( 90 \degree - \theta) = sec\theta}}$

${ \rm{6. \: cot( 90 \degree - \theta) = tan\theta}}$