CameraIcon

SearchIcon

MyQuestionIcon

152

You visited us 152 times! Enjoying our articles? Unlock Full Access!

Sign of Trigonometric Ratios in Different Quadrants

Prove the fol...

Question

Prove the following identity:
$(s i n A + s e c A)^{2} + (c o s A + c s c A)^{2} = (1 + s e c A . c s c A)^{2}$

Open in App

Solution

$L H S = (S i n A + \frac{1}{C o s A} + C o s A + \frac{1}{S i n A})$

$= {(\frac{(S i n A C o s A + 1)}{C o s A})}^{2} + {(\frac{(S i n A C o s A + 1)}{S i n A})}^{2}$

$= (\frac{(S i n A C o s A + 1)^{2}}{{C o s}^{2} A}) + (\frac{(S i n A C o s A + 1)^{2}}{{S i n}^{2} A})$

$= (S i n A C o s A + 1)^{2} * {\frac{1}{{C o s}^{2} A} + \frac{1}{{S i n}^{2} A}}$

$= {(\frac{S i n A C o s A}{S i n A C o s A} * \frac{1}{S i n A C o s A})}^{2}$

$= (1 + C o s e c A . S e c A)^{2}$

$= R H S$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Prove the following identity :

(s i n A + s e c A)^{2}

(c o s A + c o s e c A)^{2}

(1 + s e c A . c o s e c A)^{2}

Q. Prove that :

(s i n A + s e c A)^{2} + (c o s A + c o s e c A)^{2} = (1 + s e c A c o s e c A)^{2}

Q. Prove the following identity :
( sin A + sec A )² + ( cosA + cosecA )² = ( 1 + secA • cosecA )

Q. Prove the following identity.

\frac{s i n A + c o s A}{s i n A - c o s A} + \frac{s i n A - c o s A}{s i n A + c o s A} = \frac{2}{2 s i n^{2} A - 1}

(s i n A + c o s e c A)^{2} + (c o s A + s e c A)^{2} = 7 + t a n^{2} A + c o t^{2} A

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Trigonometric Functions in a Unit Circle

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Sign of Trigonometric Ratios in Different Quadrants

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon