Question

if sin A = 21÷29.evaluate secA/tanA-sinA​

Answer 1

${\huge\bf{\mid{\overline{\underline{correct\:Question}}}\mid}}$

• if SinA = 21/29 , we have to Find secA/(tanA - sinA) .

$\Large\bold\star\underline{\underline\textbf{Formula\:used}}$

• Sin A = Perpendicular/Base = P/B
• secA = Hypotenuse / Base = H/B
• TanA = Perpendicular/Base = P/B

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we know that ,,,

$\green{\large\boxed{\bold{Hypotenuse^{2} = Perpendicular^{2} + Base^{2} }}}$

since given SinA = Perpendicular/Hypotenuse = 21/29

we have ,

→ Perpendicular = P = 21

→ Hypotenuse = H = 29

Putting values we get,,,

$\red{\boxed\implies} \: {29}^{2} = {21}^{2} + B^{2} \\ \\ \red{\boxed\implies} \: B^{2} \: = {29}^{2} - {21}^{2} \\ \\ \red{\boxed\implies} \: B^{2} \: = 841 - 441 \\ \\ \red{\boxed\implies} \: B^{2} \: = 400 \\ \\ \red{\boxed\implies} \:B = \: 20$

Hence, we have now ,

→ Sec A = H/B = 29/20

→ Tan A = P/B = 21/20

→ sin A = P/H = 21/29

Putting values in Question we get,,,

$\blue{\frac{ \sec(A)}{ \tan(A) - \sin(A) }} = \green{\frac{ \frac{29}{20} }{ \frac{21}{20} - \frac{21}{29}}} \\ \\ \red{\boxed\implies} \: \: \: \: \: \: \red{\large\boxed{\bold{ \frac{841}{189} }}}$

$\large\underline\textbf{Hope it Helps You.}$