Question

If sinQ =3/5 find the value of (tanQ +secQ)²

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given ,

$\green{\fbox{ \sf \sin( \theta ) = \frac{3}{5} = \frac{p}{h} }}$

By Pythagoras theorem ,

$\sf \hookrightarrow {(h)}^{2} = {(p)}^{2} + {(b)}^{2} \\ \\ \sf \hookrightarrow</p><p> {(5)}^{2} = {(9)}^{2} + {(b)}^{2} \\ \\ \sf \hookrightarrow</p><p>25 = 9 + {(b)}^{2} </p><p> \\ \\ \sf \hookrightarrow {(b)}^{2} = 16 \\ \\ \sf \hookrightarrow </p><p>b = 4 \: \: units$

Thus , the value of base is 4 unit

So ,

$\sf \hookrightarrow {(\tan( \theta) + \sec( \theta) )}^{2} \\ \\ \sf \hookrightarrow {(\frac{p}{b} + \frac{h}{b} )}^{2} \\ \\\sf \hookrightarrow {( \frac{3}{4} + \frac{5}{4} )}^{2} \\ \\ \sf \hookrightarrow {(\frac{3 + 5}{4} )}^{2} \\ \\ \sf \hookrightarrow {(\frac{8}{4} )}^{2} \\ \\ \sf \hookrightarrow {(2)}^{2} \\ \\ \sf \hookrightarrow 4$

Therefore , the required value is 4