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Inverse Trigonometric Functions

Question

If A = sin² x + cos⁴ x, then for all real x

3/4 ≤ A ≤ 1

31/16 ≤ A ≤ 1

1≤ A ≤2

3/4 ≤ A ≤ 13/16

Solution

3/4 ≤ A ≤ 1

A = sin²x + cos⁴x = sin²x + (1 - sin² x)
2 = sin⁴x - sin²x + 1
$space equals space open parentheses space sin squared space straight x space minus space 1 half close parentheses squared space plus 3 over 4 space equals space 3 over 4 space less or equal than space straight A space less or equal than space 1$

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Inverse Trigonometric Functions

If A = sin² x + cos⁴ x, then for all real x

3/4 ≤ A ≤ 1

31/16 ≤ A ≤ 1

1≤ A ≤2

3/4 ≤ A ≤ 13/16

Some More Questions From Inverse Trigonometric Functions Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Inverse Trigonometric Functions

If A = sin2 x + cos4 x, then for all real x 3/4 ≤ A ≤ 1 31/16 ≤ A ≤ 1 1≤ A ≤2 3/4 ≤ A ≤ 13/16

Some More Questions From Inverse Trigonometric Functions Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If A = sin² x + cos⁴ x, then for all real x

3/4 ≤ A ≤ 1

31/16 ≤ A ≤ 1

1≤ A ≤2

3/4 ≤ A ≤ 13/16