Math, asked by inforajashree, 10 months ago

If tanA=(xsinB) ÷(1-xcosB) and tanB=(ysinA) ÷(1-ycosA), show that sinA/sinB=x/y

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Answers

Answered by yash5747
42

Step-by-step explanation:

Convert ... Tan A in Cot A and Cot B in tan B then simplify and substitute.

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Attachments:
Answered by bommuchakravarthilm
0

Answer:

sinA/sinB=x/y is proved by using the trigonometric formulae.

Step-by-step explanation:

We are given that

tanA=(xsinB)÷(1-xcosB)

tanB=(ysinA)÷(1-ycosA)

We are asked to show that sinA/sinB=x/y

Simply write tan in terms of cot

cotA=\frac{1-xcosB}{xsinB}

Evaluate the fraction. We get,

cotA=\frac{1}{xsinB}-\frac{xcosB}{xsinB}

Perform division.

cotA=\frac{1}{xsinB} -cotB

Bring cotB to LHS

cotA+cotB=\frac{1}{xsinB}  ---------(1)

Similarly convert tanB in terms of cotB.

cotB=\frac{1-ycosA}{ysinA}

Elaborate the terms and do division.

cotB=\frac{1}{ysinA}-\frac{ycosA}{ysinA}

On performing division for the second term. We get,

cotB=\frac{1}{ysinA} -cotA

cotA+cotB=\frac{1}{ysinA}   -------(2)

Equate (1) and (2)

\frac{1}{ysinA} =\frac{1}{xsinB}

On cross multiplication. We get,

\frac{x}{y} =\frac{sinA}{sinB}

Hence proved.

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