Question

In the following figure, if AD = 8 cm, BD = 6 cm and BC = 15 cm, then find the value of

tan^2 theta + cos^2 theta​

Answer 1

Given : AD = 8 cm, BD = 6 cm and BC = 15 cm

To Find : value of  tan² θ + cos² θ

Solution:

AD = 8

BD= 6

Apply Pythagoras theorem

AB² = AD² + BD²

=> AB² = 8² + 6²

=> AB² = 64 +36

=> AB² = 100

=> AB = 10

   BC  = 15

AC² = AB² + BC²

=> AC² = 10² + 15²

=> AC = 5√13

tan θ  = AB/BC  = 10/15  = 2/3

=> tan² θ  = (2/3)² = 4/9

cos θ  = BC/AC  = 15/5√13  = 3/√13

=>cos² θ  = ( 3/√13)² = 9/13

tan² θ + cos² θ   = (4/9) +  (9/13)  = (52 + 81)/117 = 133/117

tan² θ + cos² θ   =  133/117

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Answer 2

Answer:

this is the answer to this question of trignometry thx