Question

prove that (sinQ+cosecQ)2+(cosQ+secQ)2=7+tan2Q+cot2Q​

Answer 1

HEY MATE YOUR ANSWER IS HERE

★ CORRECT QUESTION ★

PROVE THAT

( SIN ∅ + COSEC ∅ )² + ( COS ∅ + SEC ∅)²

= 7 + TAN²∅ + COT²∅

★ SOLUTION ★

TAKING LHS

TAKING ∅ AS X

( SIN X + COSEC X )² + ( COS X + SEC X)²

IDENTITY

( a + b )² = a² + b² + 2ab

SO,

= SIN²X + COSEC²X + 2COSEC X SIN X COS²X + SEC²X + 2COS X SEC X

NOW BY TRIGNOMETRIC RATIOS

SIN ∅ × COSEC ∅ = 1

COS ∅ × SEC ∅ = 1

HENCE

= SIN²X + COSEC²X + 2(1) + COS²X + SEC²X + 2(1)

NOW REARRANGING THE EQUATION

= 4 + SIN²X + COS²X + COSEC²X + SEC²X

NOW BY TRIGNOMETRIC IDENTITY

SIN² ∅ + COS² ∅ = 1

HENCE ,

= 4 + 1 + COSEC²X + SEC²X

= 5 + COSEC²X + SEC²X

NOW AGAIN BY TRIGNOMETRIC IDENTITY

COSEC²∅ = 1 + COT² ∅

SEC²∅ = 1 + TAN² ∅

HENCE ,

=5 + ( 1 + COT²X ) + ( 1 + TAN²X )

= 5 + 1 + COT²X + 1 + TAN²X

= 7 + COT²X + TAN² X

HENCE PROVED

THANKS FOR YOUR QUESTION HOPE THIS HELPS

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