Question

Sin square A+cos square B=1 then find the value of cos square A+ square B

Answer 1

value of cos²A + sin²B = 1

explanation : your question is -> sin²A + cos²B = 1 then find value of cos²A + sin²B = ?

we know from trigonometric identities,

sin²θ + cos²θ = 1

so, sin²A + cos²A = 1

⇒sin²A = 1 - cos²A .......(1)

similarly, sin²B + cos²B = 1

⇒cos²B = 1 - sin²B ..........(1)

now given, sin²A + cos²B = 1

putting equations (1) and (2),

(1 - cos²A) + (1 - sin²B) = 1

⇒ 1 - cos²A + 1 - sin²B = 1

⇒2 - (cos²A + sin²B) = 1

⇒1 = cos²A + sin²B

hence, cos²A + sin²B = 1

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