Question

 In a ΔPQR, ∠Q=90°, if PQ = 10 cm and PR = 15 cm, then the value of tan²⁡P + sec²P + 1 is. 
(a) 5/2
(b)3/17
(c)9/2
(d)4/5​

Answer 1

Answer:

I think b is right option

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

 In a ΔPQR, ∠Q=90°, if PQ = 10 cm and PR = 15 cm, then the value of tan²⁡P + sec²P + 1 is. 

(a) 5/2

(b)3/17

(c)9/2

(d)4/5

EVALUATION

Here it is given that in a ΔPQR, ∠Q=90°, if PQ = 10 cm and PR = 15 cm

Then sec P

$\displaystyle \sf \: = \frac{PR}{PQ}$

$\displaystyle \sf \: = \frac{15}{10}$

$\displaystyle \sf \: = \frac{3}{2}$

Now we have

tan²⁡P + sec²P + 1

= 1 + tan²⁡P + sec²P

= sec²P + sec²P

= 2 sec²P

$\displaystyle \sf \: = 2 \times { \bigg(\frac{3}{2} \bigg)}^{2}$

$\displaystyle \sf \: = 2 \times \frac{9}{4}$

$\displaystyle \sf \: = \frac{9}{2}$

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf \: c) \: \: \: \frac{9}{2}$

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