Question

If 22 cos A - 3 sin A = 20 sin A, then find the value of
tan² A +sin² A . sec² A​

Answer 1

Answer:

given, 22cosA - 3sinA = 20sinA

or, 22cosA = 20sinA + 3sinA

or, 22cosA = 23sinA

or, 22/23 = sinA/cosA = tanA

so, tanA = 22/23 = p/b .......(1)

here, p = 22 and b = 23

from Pythagoras theorem,

h = √(p² + b²) = √(22² + 23²)

= √(484 + 529) = √(1013)

so, sinA = p/h = 22/√(1013) .....(2)

secA = h/b = √(1013)/23 ......(3)

now, tan²A + sin²A. sec²A

from equations (1), (2) and (3),

=(22/23)² + {22/√(1013)}² × {√(1013)/23}

= 484/529 + 484/529

= 968/529

hence, answer should be 968/529

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Answer 2

Answer:

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