If the Angles of ∆ABC Are In Ratio 1:1:2, Respectively (the largest angle being angle C) - Bzziii.com

If the angles of △ABC are in ratio 1:1:2, respectively (the largest angle being angle C), then the value of `"secA"/"cosec B"` – `"tanA"/"cot B"` is

(a) 0 

(b) 1/2 

(c) 1 

(d) √3/2

(a) 0 

Explanation:

Angles Ratio = 1:1:2

Let Angles be 

`\angle`A = x

`\angle`B = x

`\angle`A = 2x

Now,

In △ABC

By angle sum Property

`\angle`A + `\angle`B + `\angle`C = `180^{0}`

x + x + 2x = `180^{0}`

4x = `180^{0}`

x= `180^{0}/4`

x =  `45^{0}`

So, 

`\angle`A = x =  `45^{0}`

`\angle`B = x =  `45^{0}`

`\angle`C = 2x =  `90^{0}`

Now,

 `"sec A"/"cosec B"`-`"tan A"/"cot B"`

=  `"sec 45"/"cosec45"`-`"tan 45"/"cot 45"`

= `\sqrt{2}/\sqrt{2}` - `frac{1}{1}`

= 1-1

= 0

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CBSE Class 10 Mathematics Sample Paper-2022