Question

if cos theta is equal to 4 by 5 and sin theta is equal to 3 by 5 find the value of secant squared theta minus tan squared theta​

Answer 1

hope it will help you:-)

Answer 2

Sec²θ - Tan²θ  = 1  if Cosθ = 4/5  & Sinθ = 3/5

Step-by-step explanation:

Cosθ = 4/5

Sinθ = 3/5

Tanθ = Sinθ/Cosθ  = (3/5)/(4/5)

=> Tanθ =  3/4

=> Tan²θ =  (3/4)²

=> Tan²θ =   9/16

Secθ = 1/Cosθ

=> Secθ = 1/(4/5)

=> Secθ = 5/4

=> Sec²θ = (5/4)²

=> Sec²θ = 25/16

Sec²θ - Tan²θ  = 25/16 - 9/16

=> Sec²θ - Tan²θ  = (25 - 9)/16

=> Sec²θ - Tan²θ  = 16/16

=> Sec²θ - Tan²θ  = 1

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