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Question
Choose the correct alternative:
1 + cot2θ = ?
Options
tan2θ
sec2θ
cosec2θ
cos2θ
Solution
1 + cot2θ = cosec2θ
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tan2θ – sin2θ = tan2θ × sin2θ. For proof of this complete the activity given below.
Activity:
L.H.S = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 - square/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/square)`
= `tan^2theta (1 - square)`
= `tan^2theta xx square` .....[1 – cos2θ = sin2θ]
= R.H.S
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
