. show that cos square theta minus sin square theta equal to 2 tan theta upon 1 minus tan squared theta is not an identity
Answers
Step-by-step explanation:
cos²theta-sin² theta = cos(2theta)-----(1)
2tan(theta)/1-tan² theta = tan(2theta)-(2)
समीकरण (1) एवं (2) से -
cos(2theta)=tan(2theta)
जो कि नहीं होता है।
we can say that Cos²θ - Sin²θ = 2Tanθ /(1 - Tan²θ) is not an identity
Step-by-step explanation:
Cos²θ - Sin²θ = 2Tanθ /(1 - Tan²θ)
Lets put θ = 30°
Cos²30° = 3/2
Sin²30° = 1/2
Tan²30° = 1/3
Tan30° = 1/√3
Putting these value
LHS = 3/2 - 1/2 = 2/2 = 1
RHS = 2(1/√3)/(1 - 1/3) = (2/√3)(2/3) = 3/√3 = √3
1 ≠ √3
hence LHS ≠ RHS
Take other case
Lets put θ = 60°
Cos²60° = 1/2
Sin²60° = 3/2
Tan²60° = 3
Tan60° = √3
LHS = 1/2 - 3/2 = -2/2 = -1
RHS = 2(√3)/(1 - 3) = (2√3)(-2) = - √3
-1 ≠ -√3
hence LHS ≠ RHS
Hence we can say that Cos²θ - Sin²θ = 2Tanθ /(1 - Tan²θ) is not an identity
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