Raghu B.

Mathematics Tutor

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Trigonometry

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Question:

$$ Prove that (sec \theta-cosec\theta)(1+tan\theta+cot\theta)=tan\theta sec\theta-cot\theta cosec\theta$$

Raghu B.

Answer:

$$LHS=(sec \theta-cosec\theta)(1+tan\theta+cot\theta) \\ \space \space\space\space\space\space\space\space\space =( \frac{sin\theta -cos\theta}{sin\theta cos\theta})( \frac{sin\theta cos\theta+sin^2 \theta + cos^2 \theta}{sin\theta cos\theta}) \\ \space\space\space\space\space\space\space\space \space =\frac{sin^3 \theta-cos^3 \theta}{sin^2 \theta cos^2 \theta} \\ \space\space\space\space\space\space\space\space \space=tan\theta sec\theta-cot\theta cosec\theta \\ \space\space\space\space\space\space\space\space\space =RHS$$

Calculus

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Question:

$$ Diffrentiate \quad 2^{cotx} $$

Raghu B.

Answer:

$$ 2^{cotx} (ln \quad2)(-cosec^2x) $$

Differential Equations

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Question:

$$\frac{dy}{dx}=y(2x-5)$$

Raghu B.

Answer:

$$y=\exp(x^2-5x)$$

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