If sin-cos -2sin- then the value of tan - is

Given : sinθ+cosθ=√(2)sinθ ⇒sinθ+cosθsinθ=√(2) ⇒ cotθ =√(2) 1 ⇒ tanθ=1√(2) 1 =1√(2) 1×(√(2)+1)(√(2)+1) =√(2)+12 1=√(2)+1 ∴ tanθ=√(2)+1 Hence, the correct an ...

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Standard X

Mathematics

Standard Values of Trigonometric Ratios

If sinθ+cos θ...

Question

If $s i n θ + c o s θ = \sqrt{2} s i n θ,$ then the value of $t a n θ$ is

(\sqrt{2} + 1)

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(\sqrt{2} + 2)

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\sqrt{2} - 1

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Solution

The correct option is A
$(\sqrt{2} + 1)$
Given : $s i n θ + c o s θ = \sqrt{2} s i n θ \Rightarrow \frac{s i n θ + c o s θ}{s i n θ} = \sqrt{2} \Rightarrow c o t θ = \sqrt{2} - 1 \Rightarrow t a n θ = \frac{1}{\sqrt{2} - 1} = \frac{1}{\sqrt{2} - 1} \times \frac{(\sqrt{2} + 1)}{(\sqrt{2} + 1)} = \frac{\sqrt{2} + 1}{2 - 1} = \sqrt{2} + 1 ∴ t a n θ = \sqrt{2} + 1$

Hence, the correct answer is option a.

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If sinθ+cos θ=√2sinθ, then the value of tan θ is

The correct option is A (√2+1)Given : sinθ+cosθ=√2sinθ⇒sinθ+cosθsinθ=√2⇒cotθ=√2−1⇒tanθ=1√2−1=1√2−1×(√2+1)(√2+1)=√2+12−1=√2+1∴ tanθ=√2+1 Hence, the correct answer is option a.

If $s i n θ + c o s θ = \sqrt{2} s i n θ,$ then the value of $t a n θ$ is