First simplify the following expression and rewrite it in terms of sin x and cos x only: 2 /tanx+cot x . Then find in the interval x ∈ [0,π] the range of values of x for which the following inequality holds: 2 tanx+cot x < 0. Hint: The trigonometric identity for the double angle may also be helpful. [a] x ∈ ( π 2 ,π] [b] x ∈ ( π 4 ,π] [c] x ∈ (0,π] [d] x ∈ (0, π 2 ] [e] not in the list
Trigonometric Identities
Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.
Inverse Trigonometric Functions
Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.
First simplify the following expression and rewrite it in terms of sin x and cos x only: 2 /tanx+cot x .
Then find in the interval x ∈ [0,π] the range of values of x for which the following inequality holds: 2 tanx+cot x < 0.
Hint: The
[a] x ∈ ( π 2 ,π]
[b] x ∈ ( π 4 ,π]
[c] x ∈ (0,π]
[d] x ∈ (0, π 2 ]
[e] not in the list
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