If 0≤x≤π/2 and 81sin2⁡x+81cos2⁡x=30, then x is equal

# If $0\le x\le \pi /2$ and ${81}^{{\mathrm{sin}}^{2}x}+{81}^{{\mathrm{cos}}^{2}x}=30$, then is equal

1. A

$\frac{\pi }{6},\frac{\pi }{3}$

2. B

$\frac{\pi }{3},\frac{5\pi }{2}$

3. C

$\frac{5\pi }{6},\frac{\pi }{6}$

4. D

$\frac{2\pi }{3},\frac{\pi }{3}$

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

Let ${81}^{{\mathrm{sin}}^{2}x}=y$ Than,

${81}^{{\mathrm{cos}}^{2}x}={81}^{1-{\mathrm{sin}}^{2}x}=81{y}^{-1}$

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 8, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://infinitylearn.com/surge/question/mathematics/if0x2and81sin2x81cos2x30-thenxis-equal/", "fetch_time": 1675701516000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2023-06/segments/1674764500356.92/warc/CC-MAIN-20230206145603-20230206175603-00633.warc.gz", "warc_record_offset": 321654546, "warc_record_length": 12414, "token_count": 284, "char_count": 609, "score": 3.71875, "int_score": 4, "crawl": "CC-MAIN-2023-06", "snapshot_type": "latest", "language": "en", "language_score": 0.34714099764823914, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00049-of-00064.parquet"}