Question

tan square P-tan square Q=sin square P-sin square Q/cos square P ×cos square Q​

Answer 1

Solution

→ tan²P - tan²Q = (sin²P - sin²Q)/(cos²P cos²Q)

Simply break the terms.

L.H.S → sin²P/(cos²P cos²Q) - sin²Q/(cos²P cos²Q)

→ tan²P/cos²Q - tan²Q/cos²P

Since 1/cos∅ = sec∅

→ tan²P × sec²Q - tan²Q × sec²P

Since sec²∅ = tan²∅ + 1

→ tan²P(tan²Q + 1) - tan²Q(tan²P + 1)

→ tan²P tan²Q + tan²P - tan²P tan²Q - tan²Q

→ tan²P - tan²Q = R.H.S

Hence Proved

Answer 2

$\huge{\textbf{\underline{Answer:-}}}$

→ tan²P - tan²Q = (sin²P - sin²Q)/(cos²P cos²Q)

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$\huge{\textbf{\underline{Explanation:-}}}$

L.H.S → sin²P/(cos²P cos²Q) - sin²Q/(cos²P cos²Q)

→ tan²P/cos²Q - tan²Q/cos²P

Since 1/cos∅ = sec∅

→ tan²P × sec²Q - tan²Q × sec²P

Since sec²∅ = tan²∅ + 1

→ tan²P(tan²Q + 1) - tan²Q(tan²P + 1)

→ tan²P tan²Q + tan²P - tan²P tan²Q - tan²Q

→ tan²P - tan²Q = R.H.S

Hence Proved

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