Question

Prove that (sin titha +cosec titha)^2 +(cos titha +sec titha )^2 =7+tan^2 titha +cot ^2 titha

Answer 1

Hey there !!


▶ 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∅ ] .

= 5 + 1 + cot²∅ + 1 + tan²∅ .

= 7 + tan²∅ + cot²∅ = RHS.


$\huge \bf \underline{ \mathbb{LHS = RHS .}}$


✔✔ Hence, it is proved ✅✅.

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THANKS


#BeBrainly.

Answer 2

Question;



(Sin∅ + Cosec∅)² + (Cos∅+ Sec∅)² = 7+ tan²∅+ Cot²∅)

(Sin²∅+ Cosec²∅ + 2.Sin∅.Cosec∅ )+(Cos²∅+Sec²∅+2Cos.Sec∅)

(Sin²∅+Cosec²∅+2)+(Cos²∅+Sec²∅+2)

Reason; Sin∅× Cosec∅ = 1 and Cos∅×Sec∅ =1

(Sin²∅+Cos²∅)+4+(Cosec²∅+Sec²∅)

1+4+ (1+Cot²∅)+(1+tan²∅)

1+4+1+1 +tan²∅+Cot²∅

7+tan²∅+Cot²∅


Hence, LHS = RHS