3 years ago

Prove the following relations: 1) (1 - cos²A) (1 + tan²A) = tan²A

Mathematics

1 answer:

JulsSmile [24]3 years ago

7 0

Step-by-step explanation:

(1 - cos²A)(1 + tan²A) = tan²A

1 + tan²A - cos²A - cos²A · tan²A = tan²A

1 + tan²A(1 - cos²A) - cos²A = tan²A

1 - cos²A + tan²A(sin²A) = tan²A

sin²A + tan²A(sin²A) = tan²A

sin²A (1 + tan²A) = tan²A

sin²A (sec²A) = tan²A

sin²A (1/cos²A) = tan²A

(sin²A)/(cos²A) = tan²A

tan²A = tan²A → <u>Proved</u>

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Prove the following relations: 1) (1 - cos²A) (1 + tan²A) = tan²A