Question

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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

1)

▶ Prove that :-

→ ( sin∅ + cosec∅ )² + ( cos∅ + sec∅ )² = ( 7 + tan²∅ + cot²∅ .

Solution :-

We have,

LHS = ( sin∅ - cosec∅ )² + ( cos∅ - sec∅ )² .

= ( sin²∅ + cosec²∅ - 2sin∅ cosec∅ ) + ( cos²∅ + sec²∅ - 2cos∅ sec∅ ) .

= ( sin²∅ + cosec² - 2 ) + ( cos²∅ + sec²∅ - 2 ) .

[ °•° sin∅ cosec∅ = 1 and cos∅ sec∅ = 1 . ]

= sin²∅ + cosec² - 2 + cos²∅ + sec²∅ - 2 .

= ( sin²∅ + cos²∅ ) - 4 + ( cosec²∅ + sec²∅ ) .

= 1 - 4 + ( 1 + cot²∅ ) + ( 1 + tan²∅ ) .

= [ °•° sin²∅ + cos²∅ = 1, cosec²∅ = 1 + cot²∅ and sec²∅ = 1 + tan²∅ ] .

= -3 + cot²∅ + 2 + tan²∅ .

= Cot²∅ + tan²∅ - 1

= tan²∅ + cot²∅ = RHS.

2)

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