Question

Simplify(1-sinx)(1+sinx)(1+tan square x)

Answer 1

Trigonometry: Trigonometry is the study of angles and relations between angles and their sin, cos, tan, cosec, sec, cot ratios. There are many formulae for calculations:

• sin²A + cos²A = 1

• sec²A - tan²A = 1

• cosec²A - cot²A = 1

• sin2A = 2 sinA cosA

• cos2A = cos²A - sin²A

• tan2A = 2 tanA / (1 - tan²A)

• sinA * cosecA = 1

• cosA * secA = 1

• tanA * cotA = 1

Step-by-step explanation:

Now, (1 - sinx) (1 + sinx) (1 + tan²x)

= {(1 - sinx) (1 + sinx)} * sec²x [ ∵ sec²x - tan²x = 1 ]

= (1 - sin²x) * sec²x [ ∵ (a + b) (a - b) = a² - b² ]

= cos²x * sec²x [ ∵ sin²x + cos²x = 1 ]

= (cosx * secx)²

= 1²

= 1

∴ (1 - sinx) (1 + sinx) (1 + tan²x) = 1

More links:

• Prove that √{(1 - sina)/(1 + sina)} = seca - tana. - https://brainly.in/question/1808729

• What is a value of tan36° degree in trigonometry? - https://brainly.in/question/5927670

Answer 2

Explanation:

the answer is (1-sinx)(1+sinx) (1+tan2x) =1