Question

If sec theta = 4 then find the value of sin theta

Answer 1

Answer:

√15/4

Step-by-step explanation:

• secø = 4

• 1/cosø = 4

• cosø = 1/4

w.k.t cos²ø + sin²ø = 1

therefore,

• (1/4) ² + sin²ø = 1

• sin²ø = 1 - 1/16

• sin²ø = 15/16

• sinø = √15/4

Answer 2

$\mathfrak{\bf{\underline{\underline{ IDENTITES \ USED \ }}}}$

$ㅤㅤㅤㅤㅤ {sin}^{2} { \theta} + {cos}^{2} { \theta} = 1 \: \: \: \: \: \: \: \: .....(1)$

$ㅤㅤㅤㅤㅤㅤsec{ \theta} = \frac{1}{cos{ \theta}} \: \: \: \: \: \: \: \: . ......(2)$

$\mathfrak{\bf{\underline{\underline{SOLUTION \ :}}}}$

$ㅤ \impliesㅤㅤㅤㅤㅤㅤㅤ\sec( \theta) = 4 \\\impliesㅤㅤㅤㅤㅤㅤ\frac{1}{cos \theta} = 4 \\\implies ㅤㅤㅤㅤㅤ\cos( \theta) = \frac{1}{4}$

$ㅤ \implies \: ㅤㅤ{ \sin }^{2} { \theta} \: + {cos}^{2} { \theta} = 1 \: \: \: ...by \: (1)$

$\mathfrak{\bf{\underline{\underline{THEREFORE\ :}}}}$

$\implies \: \: \: \: \: \: \: \: {sin}^{2} \theta + ( { \frac{1}{4}) }^{2} = 1 \\ \implies \: \: \: \: \: \: \: \: \: \: \: {sin}^{2} \theta + \frac{1}{16} = 1 \\ \implies \: \: \: \: \: \: \: \: \: \: \: {sin}^{2} \theta = 1 - \frac{1}{16 } \ \\ \implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {sin}^{2} \theta = \frac{15}{16} \\ \implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {sin} \theta = \frac{ \sqrt{15} }{4}$

$\mathfrak{\bf{\underline{\underline{ANSWER \ :}}}}$

$\impliesㅤㅤㅤㅤ\boxed{\boxed{ \boxed{ \sin( \theta) = \frac{ \sqrt{15} }{4 } } }}$