Question

Given cot theta = 7/8
6, then evaluate (1) (1+sin theta)(1-sin theta)/
(1 + cos theta) (1 -cos theta)​

Answer 1

POINTS TO NOTICE:-

1. FOR QUESTIONS RELATED TO EVALUATING THE VALUES OF TRIGNOMETRIC FUNCTIONS
2. ASSUME OUT A RIGHT ANGLED TRIANGLE WITH PUTTUING THE VALUE OF THE FUNCTION APPLYING
3. NOW TAKING THE PYTHAGORAS THEOREM FIND OUT THE UNDETERMINED SIDE OF THE TRIANGLE
4. NOW MAKE THE TRIGNOMETRIC VALUES THAT WERE UNKMOWN
5. PUT THEM IN THEIR DESIRED FORMULAE
6. SIMPLY SOLVE IT !!

GIVEN:-

VALUE OF COT THETA = 7/8

TO FIND :-

(1 + SIN THETA)(1 - SIN THETA)

(1 + COS THETA )(1 - COS THETA)

METHOD USED:-

PYTHAGORAS THEOREM { (HYPOTENUSE)² = (PERPENDICULAR)² + (BASE)²}

SOLUTION:-

NOW WE ARE GIVEN COT THETA = 7/8

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7

AS WE KNOW THAT COT THETA = BASE / PERPENDICULAR

SO BASE / PERPENDICULAR = 7 / 8

BY PYTHAGORAS THEOREM ,

{ (HYPOTENUSE)² = (PERPENDICULAR)² + (BASE)² }

(HYPOTENUSE)² = 7² + 8²

HYPOTENUSE ² = 49 + 64

HYPOTENUSE ² = 113

HYPOTENUSE =

$\sqrt{113}$

$so \: sin \: theta \: = 8 \div \sqrt{113}$

$cos \: theta \: = 7 \div \sqrt{113}$

hence,

(1 + SIN THETA)(1 - SIN THETA)

(1 + SIN THETA)(1 - SIN THETA)(1 + COS THETA )(1 - COS THETA)

$(1 + 8 \div \sqrt{113} )(1 - 8 \div \sqrt{113} ) \div (1 + 7 \div \sqrt{113} )(1 - 7 \sqrt{113} )$

$(1 - 64 \times 113) \div (1 - 49 \times 113)$

$- 7231 \div - 5536$

1.30

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